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size="12"> <inlineAttr font-weight="normal"> <c val="#000"> Пример решения, имеющего переменную структуру. </c> </inlineAttr> </f> <f family="Times New Roman" charset="204" size="12"> <inlineAttr font-weight="normal"> <c val="#000">(</c> </inlineAttr> </f> <f family="Times New Roman Cyr" charset="204" size="12">Решение уравнений в частных производных</f> <f family="Arial Cyr" charset="204" size="12">)</f> </text> </region> <region region-id="2" left="30" top="48.75" width="456" height="119.25" align-x="30" align-y="60" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Уравнение, описывающее динамику </f> <f family="Arial Cyr" charset="204" size="12">изменения тока или напряжения в проводах,</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="5"/>представляемую<sp count="2"/>функцией "v(х,t)" переменных<sp count="2"/>"x" и "t".</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12">Для линейного дифференциального ур-я 2-го порядка в частных производных в случае двух независимых переменных, тип уравнения определяется по коэффициентам при вторых производных. 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В начальный момент времени конец<sp count="2"/>х=0<sp count="2"/>заземляется, а конец<sp count="2"/>x=L<sp count="2"/>продолжает оставаться изолированным. Найти распределение напряжения в проводе, если самоиндукция, сопротивление и емкость единицы длины известны.</inlineAttr> </f> </text> </region> <region region-id="612" left="30" top="288.75" width="119.25" height="13.5" align-x="30" align-y="300" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Задание параметров. </f> </text> </region> <region region-id="599" left="30" top="312" width="151.5" height="14.25" align-x="30" align-y="324" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Независимые параметры: </f> </text> </region> <region region-id="603" left="30" top="335.25" width="432.75" height="50.25" align-x="30" align-y="348" 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underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>.</f> </inlineAttr> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </inlineAttr> </text> </region> <region region-id="952" left="30" top="396" width="82.5" height="14.25" align-x="30" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Обозначения: </f> </text> </region> <region region-id="1098" left="132" top="396.75" width="37.5" height="15.75" align-x="145.5" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="1099" left="186" top="396.75" width="41.25" height="15.75" align-x="200.25" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="843" left="30" top="424.5" width="479.25" height="59.25" align-x="30" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Критерий выбора параметров: 1) если </f> <region region-id="846" left="243" top="425.25" width="63" height="45" align-x="255" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterThan/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="12"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> , то корни комплексные для всех n</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(N<1) и<sp count="2"/>получаем решение V4(x,t)<sp count="2"/>(</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">V5(x,t)</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">). При этом kr=5.</inlineAttr> </f> </text> </region> <region region-id="844" left="30" top="497.25" width="135.75" height="45" align-x="48" align-y="522" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">kr</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:real>5</ml:real> <ml:real>0</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="845" left="204" top="510.75" width="39" height="15.75" align-x="221.25" align-y="522" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">kr</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="14"/> </region> <region region-id="613" left="36" top="552.75" width="384.75" height="13.5" align-x="36" align-y="564" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Математическая модель. </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="10">(Вывод см. в лекциях или у Пискунова, т.2, стр.367.) </f> </text> </region> <region region-id="72" left="42" top="582.75" width="111.75" height="20.25" align-x="68.25" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve" subscript="xx">V</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="tt">V</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t">V</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="15"/> </region> <region region-id="92" left="216" top="582.75" width="51.75" height="15.75" align-x="251.25" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessOrEqual/> <ml:apply> <ml:lessOrEqual/> <ml:real>0</ml:real> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </math> <rendering item-idref="16"/> </region> <region region-id="93" left="312" top="582.75" width="25.5" height="15.75" align-x="322.5" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterThan/> <ml:id xml:space="preserve">t</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="17"/> </region> <region region-id="130" left="474" top="582.75" width="15.75" height="15.75" align-x="480.75" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </ml:parens> </math> <rendering item-idref="18"/> </region> <region region-id="615" left="30" top="612.75" width="450.75" height="46.5" align-x="30" align-y="624" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Здесь: V(x,t) - напряжение в сечении провода с координатой х в момент времени t;</f> <f family="Arial Cyr" charset="204" size="12">A</f> <f family="Arial Cyr" charset="204" size="12"> 12 </f> <f family="Arial Cyr" charset="204" size="12">=0; </f> <f family="Arial Cyr" charset="204" size="12">A</f> <f family="Arial Cyr" charset="204" size="12"> 11 </f> <f family="Arial Cyr" charset="204" size="12">=-c*J; </f> <f family="Arial Cyr" charset="204" size="12">A2</f> <f family="Arial Cyr" charset="204" size="12"> 2 </f> <f family="Arial Cyr" charset="204" size="12"> 2 </f> <f family="Arial Cyr" charset="204" size="12">=1.<sp count="2"/>Поэтому (Д=c*J>0)<sp count="2"/>уравнение (1) имеет гиперболический</f> <f family="Arial Cyr" charset="204" size="12">тип. V</f> <f family="Arial Cyr" charset="204" size="12"> xx </f> <f family="Arial Cyr" charset="204" size="12"> - </f> <f family="Arial Cyr" charset="204" size="12">вторая </f> <f family="Arial Cyr" charset="204" size="12">частная производная по х, V</f> <f family="Arial Cyr" charset="204" size="12"> tt </f> <f family="Arial Cyr" charset="204" size="12"> - тоже по t, и т. д.</f> </text> </region> <region region-id="99" left="42" top="672" width="204.75" height="14.25" align-x="42" align-y="684" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Краевые условия: </f> </text> </region> <region region-id="100" left="42" top="708.75" width="66" height="15.75" align-x="84.75" align-y="720" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">V</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> </math> <rendering item-idref="19"/> </region> <region region-id="107" left="132" top="708.75" width="60.75" height="20.25" align-x="177.75" align-y="720" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="t">V</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:sequence> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="20"/> </region> <region region-id="108" left="216" top="708.75" width="108.75" height="13.5" align-x="216" align-y="720" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Начальные условия</f> </text> </region> <region region-id="1113" left="474" top="738.75" width="15.75" height="15.75" align-x="480.75" align-y="750" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>2</ml:real> </ml:parens> </math> <rendering item-idref="21"/> </region> <region region-id="102" left="48" top="750.75" width="55.5" height="15.75" align-x="88.5" align-y="762" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">V</ml:id> <ml:sequence> <ml:real>0</ml:real> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="22"/> </region> <region region-id="103" left="120" top="750.75" width="61.5" height="20.25" align-x="166.5" align-y="762" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="x">V</ml:id> <ml:sequence> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="23"/> </region> <region region-id="110" left="216" top="750.75" width="106.5" height="13.5" align-x="216" align-y="762" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Граничные условия</f> </text> </region> <region region-id="114" left="42" top="786" width="129" height="14.25" align-x="42" align-y="798" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12"> Решение </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false"> ищем в виде:</inlineAttr> </f> </text> </region> <region region-id="617" left="204" top="786.75" width="95.25" height="15.75" align-x="243.75" align-y="798" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">V</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="24"/> </region> <region region-id="637" left="474" top="786.75" width="28.5" height="15.75" align-x="487.5" align-y="798" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">resh</ml:id> </ml:parens> </math> <rendering item-idref="25"/> </region> <region region-id="619" left="42" top="810.75" width="352.5" height="13.5" align-x="42" align-y="822" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Исходя из краевых условий (2), запишем следующие выражения:</f> </text> </region> <region region-id="631" left="54" top="834.75" width="80.25" height="15.75" align-x="75.75" align-y="846" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">V0</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="26"/> </region> <region region-id="632" left="156" top="834.75" width="74.25" height="15.75" align-x="169.5" align-y="846" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:real>0</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T'</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="27"/> </region> <region region-id="956" left="462" top="846.75" width="21" height="15.75" align-x="471.75" align-y="858" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:mult style="auto-select"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:parens> </math> <rendering item-idref="28"/> </region> <region region-id="1084" left="54" top="864.75" width="69.75" height="15.75" align-x="67.5" align-y="876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:real>0</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="29"/> </region> <region region-id="628" left="150" top="864.75" width="72.75" height="15.75" align-x="163.5" align-y="876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:real>0</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">X'</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="30"/> </region> <region region-id="1082" left="36" top="894" width="461.25" height="43.5" align-x="36" align-y="906" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Из этих равенств следует, что </f> <region region-id="635" left="202.5" top="894.75" width="45.75" height="15.75" align-x="233.25" align-y="906" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="31"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> и </inlineAttr> </f> <region region-id="636" left="261" top="894.75" width="42" height="15.75" align-x="288" align-y="906" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="32"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. В противном случае мы </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">получаем </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">тривиальное (нулевое) решение. Подстановка (resh) в (1) приводит </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">к двум линейным дифференциальным </f> </inlineAttr> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">уравнениям 2-го порядка:</f> </inlineAttr> </text> </region> <region region-id="649" left="42" top="960.75" width="76.5" height="13.5" align-x="42" align-y="972" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Первое из них</f> </text> </region> <region region-id="648" left="138" top="945.75" width="115.5" height="44.25" align-x="238.5" align-y="972" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="33"/> </region> <region region-id="653" left="462" top="966.75" width="15.75" height="15.75" align-x="468.75" align-y="978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>3</ml:real> </ml:parens> </math> <rendering item-idref="34"/> </region> <region region-id="650" left="42" top="1002.75" width="140.25" height="13.5" align-x="42" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">с начальными условиями:</f> </text> </region> <region region-id="652" left="198" top="1002.75" width="46.5" height="15.75" align-x="229.5" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="35"/> </region> <region region-id="651" left="276" top="1002.75" width="49.5" height="15.75" align-x="310.5" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">X'</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="36"/> </region> <region region-id="656" left="42" top="1029" width="476.25" height="70.5" align-x="42" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">позволяет найти </f> <region region-id="655" left="134.25" top="1038.75" width="53.25" height="17.25" align-x="165" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="37"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> ,<sp count="2"/>где<sp count="2"/> </inlineAttr> </f> <region region-id="657" left="224.25" top="1035.75" width="84" height="20.25" align-x="245.25" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:sqrt/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="38"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">,<sp count="3"/> </inlineAttr> </f> <region region-id="658" left="321" top="1029.75" width="96" height="34.5" align-x="350.25" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:sqrt/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="39"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/> </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">П</f> </inlineAttr> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">оследние </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12">называют:</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="661" left="165" top="1065" width="13.5" height="18" align-x="171" align-y="1077" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="40"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> -</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="3"/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">собственными значениями </f> <f family="Arial Cyr" charset="204" size="12"> и</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>соответствующие им </f> <f family="Arial Cyr" charset="204" size="12">Х</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">(x) - </f> <f family="Arial Cyr" charset="204" size="12">собственными функциями</f> <f family="Arial Cyr" charset="204" size="12">.</f> </text> </region> <region region-id="690" left="42" top="1110.75" width="441.75" height="43.5" align-x="42" align-y="1122" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Причём {X</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">} представляет систему ортогональных функций на отрезке [-2L,2L], а</f> <f family="Arial Cyr" charset="204" size="12">также на отрезках: </f> <f family="Arial Cyr" charset="204" size="12">[0,2L] или </f> <f family="Arial Cyr" charset="204" size="12">[-L,L], </f> <f family="Arial Cyr" charset="204" size="12">[0,L] или</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">[-L/2,L/2] (см. файл: "СистОртогФункций"\</f> <f family="Arial Cyr" charset="204" size="12">"СистОртогФункций.xmcd".</f> </text> </region> <region region-id="675" left="174" top="1173.75" width="101.25" height="34.5" align-x="223.5" align-y="1194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:parens> </math> <rendering item-idref="41"/> </region> <region region-id="676" left="300" top="1182.75" width="52.5" height="15.75" align-x="341.25" align-y="1194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:sequence xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:real>2</ml:real> <ml:id xml:space="preserve" font="1">...</ml:id> </ml:sequence> </math> <rendering item-idref="42"/> </region> <region region-id="677" left="456" top="1182.75" width="15.75" height="15.75" align-x="462.75" align-y="1194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>4</ml:real> </ml:parens> </math> <rendering item-idref="43"/> </region> <region region-id="1051" left="48" top="1224.75" width="344.25" height="13.5" align-x="48" align-y="1236" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Правда, для указанных выше отрезков, нормы будут разными: </f> </text> </region> <region region-id="1054" left="48" top="1254.75" width="314.25" height="61.5" align-x="71.25" align-y="1290" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">nor</ml:id> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:bounds> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">substitute</ml:id> <ml:apply> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </ml:sequence> </ml:command> <ml:command> <ml:id xml:space="preserve">simplify</ml:id> </ml:command> <ml:symResult> <ml:id xml:space="preserve">π</ml:id> </ml:symResult> </ml:symEval> </ml:define> </math> <rendering item-idref="44"/> </region> <region region-id="1067" left="432" top="1278.75" width="21" height="15.75" align-x="441.75" align-y="1290" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:mult style="auto-select"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:parens> </math> <rendering item-idref="45"/> </region> <region region-id="1068" left="438" top="1344.75" width="21.75" height="15.75" align-x="447.75" align-y="1356" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real base="2">4</ml:real> </ml:parens> </math> <rendering item-idref="46"/> </region> <region region-id="1057" left="48" top="1332.75" width="339" height="61.5" align-x="77.25" align-y="1368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">nor1</ml:id> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:bounds> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">substitute</ml:id> <ml:apply> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </ml:sequence> </ml:command> <ml:command> <ml:id xml:space="preserve">simplify</ml:id> </ml:command> <ml:symResult> <ml:apply> <ml:mult style="narrow-dot"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:symResult> </ml:symEval> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="1059" left="54" top="1416.75" width="329.25" height="13.5" align-x="54" align-y="1428" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Нас интересует отрезок [0,L] и соответствующая ему норма.</f> </text> </region> <region region-id="659" left="42" top="1457.25" width="462" height="18.75" align-x="42" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Второе из уравнений с учётом найденного значения </f> <region region-id="694" left="327" top="1458" width="13.5" height="18" align-x="333" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="48"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> будет иметь вид:</inlineAttr> </f> </text> </region> <region region-id="691" left="42" top="1485.75" width="184.5" height="44.25" align-x="211.5" align-y="1512" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="49"/> </region> <region region-id="692" left="264" top="1500.75" width="27.75" height="15.75" align-x="276.75" align-y="1512" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:id xml:space="preserve">a</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="50"/> </region> <region region-id="693" left="366" top="1500.75" width="15.75" height="15.75" align-x="372.75" align-y="1512" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>5</ml:real> </ml:parens> </math> <rendering item-idref="51"/> </region> <region region-id="151" left="36" top="1547.25" width="439.5" height="45.75" align-x="36" align-y="1560" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Находим решение (5) , которое будет зависеть от значения </f> <region region-id="159" left="361.5" top="1548" width="13.5" height="18" align-x="367.5" align-y="1560" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="52"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Для этого найдем корни характеристического уравнения, соответствующего уравнению (5).</inlineAttr> </f> </text> </region> <region region-id="252" left="48" top="1602" width="77.25" height="18" align-x="72.75" align-y="1614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="53"/> </region> <region region-id="253" left="174" top="1602" width="76.5" height="18" align-x="198.75" align-y="1614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p2</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="54"/> </region> <region region-id="254" left="294" top="1602.75" width="52.5" height="15.75" align-x="335.25" align-y="1614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:sequence xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:real>2</ml:real> <ml:id xml:space="preserve" font="1">...</ml:id> </ml:sequence> </math> <rendering item-idref="55"/> </region> <region region-id="273" left="480" top="1602.75" width="15.75" height="15.75" align-x="486.75" align-y="1614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>6</ml:real> </ml:parens> </math> <rendering item-idref="56"/> </region> <region region-id="291" left="42" top="1656.75" width="27" height="13.5" align-x="42" align-y="1668" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">где: </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="299" left="78" top="1648.5" width="43.5" height="33.75" align-x="93.75" align-y="1668" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ν</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">R</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="57"/> </region> <region region-id="304" left="144" top="1641" width="198" height="47.25" align-x="167.25" align-y="1668" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="58"/> </region> <region region-id="305" left="474" top="1656.75" width="15.75" height="15.75" align-x="480.75" align-y="1668" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>7</ml:real> </ml:parens> </math> <rendering item-idref="59"/> </region> <region region-id="695" left="30" top="1710.75" width="488.25" height="27" align-x="30" align-y="1722" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">В зависимости от выбора параметров и, что самое главное, от значений индекса "n", корни (6) могут быть как действительными разными или равными, так и комплексными. </f> </text> </region> <region region-id="268" left="24" top="1750.5" width="406.5" height="96.75" align-x="24" align-y="1776" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Поэтому найдем такое n, при котором </f> <region region-id="261" left="233.25" top="1751.25" width="117.75" height="45" align-x="336" align-y="1776" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="60"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Или </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="267" left="27" top="1797" width="86.25" height="36.75" align-x="39.75" align-y="1818.75" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">R</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="61"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> .</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Обозначим это значение через N</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="266" left="132" top="1862.25" width="92.25" height="36.75" align-x="149.25" align-y="1884" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">R</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="62"/> </region> <region region-id="577" left="264" top="1872.75" width="47.25" height="15.75" align-x="280.5" align-y="1884" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.5</ml:real> </result> </ml:eval> </math> <rendering item-idref="63"/> </region> <region region-id="696" left="486" top="1872.75" width="15.75" height="15.75" align-x="492.75" align-y="1884" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>8</ml:real> </ml:parens> </math> <rendering item-idref="64"/> </region> <region region-id="578" left="24" top="1922.25" width="466.5" height="12" align-x="24" align-y="1932" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">Примечание. Можно подогнать R так, чтобы N было целым. Для этого R будем вычислять по формуле:</f> </text> </region> <region region-id="579" left="36" top="1952.25" width="148.5" height="36" align-x="59.25" align-y="1974" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">RR</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">ceil</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">J</ml:id> <ml:id xml:space="preserve">c</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="65"/> </region> <region region-id="580" left="222" top="1962.75" width="53.25" height="15.75" align-x="244.5" align-y="1974" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">RR</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.5</ml:real> </result> </ml:eval> </math> <rendering item-idref="66"/> </region> <region region-id="581" left="30" top="2000.25" width="477" height="12" align-x="30" align-y="2010" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">Полученное значение R=RR надо подставить в исходные данные в начале листинга. Конец Примечания.</f> </text> </region> <region region-id="278" left="30" top="2034.75" width="423" height="27" align-x="30" align-y="2046" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Значения (8) приводят к разбиению множества индексов n<sp count="2"/>на подмножества.</f> <f family="Arial Cyr" charset="204" size="12">Учитывая (8), решение уравнения (5) запишется в следующем виде:</f> </text> </region> <region region-id="279" left="36" top="2130" width="343.5" height="20.25" align-x="36" align-y="2142" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> 1) Для </f> <region region-id="166" left="75" top="2130.75" width="30.75" height="15.75" align-x="87.75" align-y="2142" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessThan/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </math> <rendering item-idref="67"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (корни p1</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, p2</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>действительные разные)</inlineAttr> </f> </text> </region> <region region-id="309" left="36" top="2158.5" width="218.25" height="25.5" align-x="80.25" align-y="2178" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">T1</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="68"/> </region> <region region-id="311" left="282" top="2166.75" width="112.5" height="13.5" align-x="282" align-y="2178" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">или, что одно и тоже:</f> </text> </region> <region region-id="281" left="36" top="2196.75" width="246.75" height="23.25" align-x="80.25" align-y="2214" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">T1</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="69"/> </region> <region region-id="284" left="480" top="2202.75" width="15.75" height="15.75" align-x="486.75" align-y="2214" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>9</ml:real> </ml:parens> </math> <rendering item-idref="70"/> </region> <region region-id="316" left="36" top="2232" width="205.5" height="18" align-x="36" align-y="2244" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">где: </f> <region region-id="314" left="60" top="2232.75" width="81.75" height="17.25" align-x="81" align-y="2244" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="71"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> ,<sp count="2"/> </inlineAttr> </f> <region region-id="315" left="154.5" top="2232.75" width="80.25" height="17.25" align-x="174.75" align-y="2244" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="72"/> </region> </text> </region> <region region-id="180" left="42" top="2268" width="243" height="20.25" align-x="42" align-y="2280" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> 2) Для </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="197" left="81" top="2268.75" width="30.75" height="15.75" align-x="93.75" align-y="2280" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterThan/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </math> <rendering item-idref="73"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">(корни </f> <f family="Arial Cyr" charset="204" size="12">p1</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">, p2</f> <f family="Arial Cyr" charset="204" size="12">n</f> <f family="Arial Cyr" charset="204" size="12"> комплексные)</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="322" left="288" top="2253" width="196.5" height="47.25" align-x="309.75" align-y="2280" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="74"/> </region> <region region-id="286" left="48" top="2304.75" width="233.25" height="23.25" align-x="92.25" align-y="2322" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">T2</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="75"/> </region> <region region-id="287" left="480" top="2310.75" width="21.75" height="15.75" align-x="489.75" align-y="2322" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>10</ml:real> </ml:parens> </math> <rendering item-idref="76"/> </region> <region region-id="318" left="42" top="2340" width="432.75" height="33" align-x="42" align-y="2352" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> 3) Для </f> <region region-id="333" left="81" top="2340.75" width="30.75" height="15.75" align-x="93.75" align-y="2352" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </math> <rendering item-idref="77"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>(так как n по определению целое число, то в этом случае и<sp count="3"/>N<sp count="2"/>также целое, и корни p1</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, p2</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>действительные равные)</inlineAttr> </f> </text> </region> <region region-id="327" left="60" top="2388.75" width="140.25" height="23.25" align-x="104.25" align-y="2406" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">T3</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="78"/> </region> <region region-id="324" left="486" top="2394.75" width="21.75" height="15.75" align-x="495.75" align-y="2406" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>11</ml:real> </ml:parens> </math> <rendering item-idref="79"/> </region> <region region-id="1103" left="36" top="2426.25" width="398.25" height="56.25" align-x="36" align-y="2448" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">Примечание:<sp count="2"/> </f> <region region-id="1102" left="100.5" top="2427" width="236.25" height="36.75" align-x="156" align-y="2448" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">T3</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="80"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. При </inlineAttr> </f> <region region-id="1104" left="363.75" top="2436.75" width="25.5" height="15.75" align-x="374.25" align-y="2448" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">t</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="81"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> получим</inlineAttr> </f> <region region-id="1105" left="36" top="2464.5" width="80.25" height="18" align-x="101.25" align-y="2476.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="82"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="957" left="30" top="2502.75" width="444" height="64.5" align-x="30" align-y="2514" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Так как в каждом случае </f> <f family="Arial Cyr" charset="204" size="12"> 1), 2), 3) </f> <f family="Arial Cyr" charset="204" size="12"> индекы </f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12"> разные, то это даёт н</f> <f family="Arial Cyr" charset="204" size="12">ам </f> <f family="Arial Cyr" charset="204" size="12">возможность записывать в вектор</f> <f family="Arial Cyr" charset="204" size="12">, в общем случае различные,<sp count="2"/>коэффициенты </f> <region region-id="329" left="393.75" top="2517.75" width="14.25" height="17.25" align-x="399.75" align-y="2529" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="83"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">, </f> </inlineAttr> <region region-id="330" left="414.75" top="2517.75" width="13.5" height="17.25" align-x="420.75" align-y="2529" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="84"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>равно как и </f> </inlineAttr> <region region-id="331" left="59.25" top="2535.75" width="15" height="18" align-x="66" align-y="2547.75" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="85"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> , обозначение которых вместе с самой функцией T(t,n) можно оставить единым для всех трех случаев.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="698" left="30" top="2574.75" width="465.75" height="34.5" align-x="30" align-y="2586" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Подставим найденные X</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">(x)</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>и T</f> <f family="Arial Cyr" charset="204" size="12">(t,n) в (resh) и, используя начальные условия в (2), запишем два уравнения для </f> <f family="Arial Cyr" charset="204" size="12">определения к</f> <f family="Arial Cyr" charset="204" size="12">оэффициентов </f> <region region-id="335" left="351" top="2592" width="14.25" height="17.25" align-x="357" align-y="2603.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="86"/> </region> <f family="Arial Cyr" charset="204" size="12">, </f> <region region-id="336" left="372" top="2592" width="13.5" height="17.25" align-x="378" align-y="2603.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="87"/> </region> </text> </region> <region region-id="346" left="36" top="2625" width="196.5" height="51" align-x="209.25" align-y="2652" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:sequence> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">∞</ml:id> </ml:bounds> </ml:apply> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> </math> <rendering item-idref="88"/> </region> <region region-id="348" left="270" top="2640.75" width="58.5" height="15.75" align-x="313.5" align-y="2652" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">T'</ml:id> <ml:sequence> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="89"/> </region> <region region-id="350" left="474" top="2640.75" width="21.75" height="15.75" align-x="483.75" align-y="2652" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>12</ml:real> </ml:parens> </math> <rendering item-idref="90"/> </region> <region region-id="713" left="24" top="2688.75" width="476.25" height="83.25" align-x="24" align-y="2700" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Константу V0, заданную на интервале 0<x<L, доопределим нечётным образом на отрезке </f> <f family="Arial Cyr" charset="204" size="12">(-L,0) и р</f> <f family="Arial Cyr" charset="204" size="12">азложим в ряд Фурье<sp count="3"/>по собственным функциям </f> <region region-id="352" left="390.75" top="2703" width="14.25" height="17.25" align-x="396.75" align-y="2714.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="91"/> </region> <f family="Arial Cyr" charset="204" size="12">:</f> <region region-id="370" left="24" top="2721" width="185.25" height="51" align-x="45.75" align-y="2748" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">V0</ml:id> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">V1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">∞</ml:id> </ml:bounds> </ml:apply> </ml:apply> </math> <rendering item-idref="92"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> .<sp count="6"/> </inlineAttr> </f> </text> </region> <region region-id="1060" left="30" top="2832.75" width="476.25" height="108" align-x="30" align-y="2844" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">В общем случае коэффициент ряда Фурье V1</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12"> функции V0 определяется так:</f> <region region-id="1061" left="30" top="2850" width="129" height="90.75" align-x="57" align-y="2898" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">V1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">V0</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:bounds> </ml:apply> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:bounds> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="93"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, здесь </inlineAttr> </f> <region region-id="1062" left="200.25" top="2886" width="23.25" height="16.5" align-x="207.75" align-y="2898" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </math> <rendering item-idref="94"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> - вес собственной функции </inlineAttr> </f> <region region-id="1064" left="376.5" top="2886.75" width="14.25" height="17.25" align-x="382.5" align-y="2898" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="95"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, равный единице.</inlineAttr> </f> </text> </region> <region region-id="1069" left="30" top="2970.75" width="219" height="13.5" align-x="30" align-y="2982" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Используя формулы (4a) и (4b), найдём:</f> </text> </region> <region region-id="1077" left="288" top="2970" width="42" height="16.5" align-x="311.25" align-y="2982" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">nor</ml:id> <ml:symResult> <ml:id xml:space="preserve">π</ml:id> </ml:symResult> </ml:symEval> </math> <rendering item-idref="96"/> </region> <region region-id="1078" left="348" top="2970" width="57.75" height="16.5" align-x="377.25" align-y="2982" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">nor1</ml:id> <ml:symResult> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="97"/> </region> <region region-id="1085" left="30" top="3000.75" width="403.5" height="55.5" align-x="72.75" align-y="3030" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V1a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> </ml:function> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">nor</ml:id> </ml:apply> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">V0</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:bounds> </ml:apply> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">substitute</ml:id> <ml:apply> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </ml:sequence> </ml:command> <ml:symResult> <ml:apply> <ml:div/> <ml:real>4</ml:real> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </ml:define> </math> <rendering item-idref="98"/> </region> <region region-id="1091" left="36" top="3099" width="428.25" height="64.5" align-x="79.5" align-y="3132" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V1b</ml:id> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> </ml:function> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">nor1</ml:id> </ml:apply> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">V0</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:bounds> </ml:apply> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">substitute</ml:id> <ml:apply> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </ml:sequence> </ml:command> <ml:command> <ml:sequence> <ml:id xml:space="preserve">substitute</ml:id> <ml:apply> <ml:equal/> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:sequence> </ml:command> <ml:command> <ml:id xml:space="preserve">simplify</ml:id> </ml:command> <ml:symResult> <ml:apply> <ml:div/> <ml:real>4</ml:real> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </ml:define> </math> <rendering item-idref="99"/> </region> <region region-id="1092" left="36" top="3186.75" width="466.5" height="62.25" align-x="36" align-y="3198" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Из полученных значений коэффициентов ряда Фурье следует то, что константу V0</f> <f family="Arial Cyr" charset="204" size="12">не обязательно было доопределять как нечетную функцию на отрезке [-L,0]. </f> <f family="Arial Cyr" charset="204" size="12">Далее за коэффициент ряда Фурье примем: </f> <region region-id="1093" left="280.5" top="3214.5" width="93.75" height="34.5" align-x="307.5" align-y="3234" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">V1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="100"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> </text> </region> <region region-id="516" left="36" top="3270.75" width="394.5" height="13.5" align-x="36" align-y="3282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Построим график функции VK(x), представляющий данную константу V0:</f> </text> </region> <region region-id="514" left="54" top="3297.75" width="255.75" height="50.25" align-x="94.5" align-y="3324" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">VK</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">V0</ml:id> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>4</ml:real> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:real>100</ml:real> </ml:bounds> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="101"/> </region> <region region-id="515" left="354" top="3318.75" width="92.25" height="15.75" align-x="403.5" align-y="3330" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">VK</ml:id> <ml:real>1.9</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.99487283758323108</ml:real> </result> </ml:eval> </math> <rendering item-idref="102"/> </region> <region region-id="548" left="474" top="3318.75" width="21.75" height="15.75" align-x="483.75" align-y="3330" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>13</ml:real> </ml:parens> </math> <rendering item-idref="103"/> </region> <region region-id="519" left="54" top="3354" width="176.25" height="115.5" align-x="54" align-y="3354" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="104"/> <rendering item-idref="105"/> </region> <region region-id="1107" left="288" top="3396.75" width="190.5" height="30" align-x="288" align-y="3408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Здесь 2L - полупериод, так как</f> <region region-id="848" left="288" top="3411" width="33" height="15.75" align-x="305.25" align-y="3422.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">VK</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </math> <rendering item-idref="106"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> имеет период 4L</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">.</f> </text> </region> <region region-id="699" left="36" top="3510.75" width="227.25" height="13.5" align-x="36" align-y="3522" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Таким образом, получены два уравнения:</f> </text> </region> <region region-id="707" left="42" top="3546.75" width="69.75" height="17.25" align-x="83.25" align-y="3558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:sequence> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">V1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="107"/> </region> <region region-id="708" left="162" top="3546.75" width="58.5" height="15.75" align-x="205.5" align-y="3558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">T'</ml:id> <ml:sequence> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="108"/> </region> <region region-id="1115" left="420" top="3546.75" width="27" height="15.75" align-x="432.75" align-y="3558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:mult style="auto-select"/> <ml:real>12</ml:real> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:parens> </math> <rendering item-idref="109"/> </region> <region region-id="1108" left="36" top="3576.75" width="476.25" height="43.5" align-x="36" align-y="3588" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">из которых следует искать коэффициенты A</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12"> и B</f> <f family="Arial Cyr" charset="204" size="12"> n , </f> <f family="Arial Cyr" charset="204" size="12"> Определение<sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12">A</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12"> и B</f> <f family="Arial Cyr" charset="204" size="12">n </f> <f family="Arial Cyr" charset="204" size="12">будет </f> <f family="Arial Cyr" charset="204" size="12">дано ниже</f> <f family="Arial Cyr" charset="204" size="12">. Само же решение (resh), исходя из принципа суперпозиции теперь </f> <f family="Arial Cyr" charset="204" size="12">будет иметь вид:</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="716" left="432" top="3642.75" width="32.25" height="15.75" align-x="447" align-y="3654" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Resh</ml:id> </ml:parens> </math> <rendering item-idref="110"/> </region> <region region-id="715" left="150" top="3633" width="211.5" height="51" align-x="189.75" align-y="3660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">V</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">∞</ml:id> </ml:bounds> </ml:apply> </ml:apply> </math> <rendering item-idref="111"/> </region> <region region-id="719" left="30" top="3696.75" width="455.25" height="43.5" align-x="30" align-y="3708" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Функция V(х,t) является нечетной периодической с периодом 4L (2L - полупериод) и представлена рядом Фурье в виде разложения по системе ортогональных функций {X</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">}</f> <f family="Arial Cyr" charset="204" size="12"> .</f> </text> </region> <region region-id="465" left="150" top="3756.75" width="159" height="14.25" align-x="150" align-y="3768" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Алгоритмизация решения. </f> </text> </region> <region region-id="964" left="42" top="3780.75" width="411.75" height="13.5" align-x="42" align-y="3792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Все задаваемые ниже параметры можно менять в интерактивном режиме.</f> </text> </region> <region region-id="961" left="42" top="3804.75" width="230.25" height="13.5" align-x="42" align-y="3816" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Зададим диапазон изменения индекса "n":</f> </text> </region> <region region-id="962" left="288" top="3804.75" width="54.75" height="15.75" align-x="314.25" align-y="3816" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">NN</ml:id> <ml:real>150</ml:real> </ml:define> </math> <rendering item-idref="112"/> </region> <region region-id="963" left="360" top="3804.75" width="57.75" height="15.75" align-x="373.5" align-y="3816" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">n</ml:id> <ml:range> <ml:real>1</ml:real> <ml:id xml:space="preserve">NN</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="113"/> </region> <region region-id="850" left="42" top="3827.25" width="450.75" height="17.25" align-x="42" align-y="3840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Погрешность округления<sp count="2"/>N до целого числа: </f> <region region-id="1002" left="288" top="3828" width="52.5" height="16.5" align-x="303" align-y="3840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIFunction" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ε</ml:id> <ml:real>0.001</ml:real> </ml:define> </math> <rendering item-idref="114"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Её можно задать как ноль.</inlineAttr> </f> </text> </region> <region region-id="733" left="42" top="3868.5" width="105" height="39.75" align-x="63" align-y="3894" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="115"/> </region> <region region-id="732" left="174" top="3867" width="200.25" height="47.25" align-x="198" align-y="3894" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="116"/> </region> <region region-id="546" left="42" top="3933" width="198.75" height="47.25" align-x="64.5" align-y="3960" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="117"/> </region> <region region-id="362" left="36" top="3990" width="441.75" height="31.5" align-x="36" align-y="4002" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Следовательно (см. (12а)), </f> <region region-id="363" left="186.75" top="3990.75" width="69.75" height="17.25" align-x="228" align-y="4002" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:sequence> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">V1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="118"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> и для всех случаев (всех n) </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false" line-through="false">1), 2), 3)</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> имеем:</inlineAttr> </f> </text> </region> <region region-id="476" left="108" top="4036.5" width="90" height="34.5" align-x="129.75" align-y="4056" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="119"/> </region> <region region-id="378" left="468" top="4050.75" width="21.75" height="15.75" align-x="477.75" align-y="4062" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>14</ml:real> </ml:parens> </math> <rendering item-idref="120"/> </region> <region region-id="855" left="42" top="4086.75" width="321.75" height="13.5" align-x="42" align-y="4098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Проверка и вывод на экран монитора численных значений:</f> </text> </region> <region region-id="856" left="384" top="4086.75" width="69" height="17.25" align-x="410.25" align-y="4098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:real>50</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.012861005502375381</ml:real> </result> </ml:eval> </math> <rendering item-idref="121"/> </region> <region region-id="858" left="42" top="4110.75" width="474.75" height="37.5" align-x="42" align-y="4122" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Второе условие в (12) даст </f> <f family="Arial Cyr" charset="204" size="12">для всех случаев (всех n) </f> <f family="Arial Cyr" charset="204" size="12"> 1), 2), 3) </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal">, считая для случая 3) </inlineAttr> </f> <region region-id="379" left="42" top="4125.75" width="39.75" height="18" align-x="66.75" align-y="4137.75" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="122"/> </region> <f family="Arial Cyr" charset="204" size="12"> : </f> <region region-id="381" left="90" top="4125.75" width="90.75" height="18" align-x="165.75" align-y="4137.75" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">ν</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="123"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false" line-through="false">. </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Что в свою очередь позволит вычислить B</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="1114" left="42" top="4158" width="448.5" height="36.75" align-x="42" align-y="4170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> 1а) Для </f> <region region-id="391" left="87.75" top="4158.75" width="30.75" height="15.75" align-x="100.5" align-y="4170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessThan/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </math> <rendering item-idref="124"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (корни p1</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, p2</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>действительные разные). </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">Введем константы N1, N2 и К для вычисления В</f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, записываемых в вектор В</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> </text> </region> <region region-id="449" left="48" top="4244.25" width="133.5" height="36.75" align-x="71.25" align-y="4266" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N1</ml:id> <ml:apply> <ml:id xml:space="preserve">floor</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="125"/> </region> <region region-id="862" left="210" top="4254.75" width="67.5" height="15.75" align-x="233.25" align-y="4266" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N2</ml:id> <ml:apply> <ml:id xml:space="preserve">ceil</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="126"/> </region> <region region-id="863" left="42" top="4290.75" width="321.75" height="13.5" align-x="42" align-y="4302" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Проверка и вывод на экран монитора численных значений:</f> </text> </region> <region region-id="871" left="42" top="4320.75" width="44.25" height="15.75" align-x="64.5" align-y="4332" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N1</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="127"/> </region> <region region-id="872" left="126" top="4320.75" width="44.25" height="15.75" align-x="148.5" align-y="4332" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N2</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>2</ml:real> </result> </ml:eval> </math> <rendering item-idref="128"/> </region> <region region-id="873" left="210" top="4320.75" width="47.25" height="15.75" align-x="226.5" align-y="4332" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.5</ml:real> </result> </ml:eval> </math> <rendering item-idref="129"/> </region> <region region-id="861" left="36" top="4345.5" width="456.75" height="75" align-x="36" align-y="4368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Таким образом, N1 - это наибольшее целое число, не превосходящее<sp count="2"/> </f> <region region-id="271" left="421.5" top="4346.25" width="65.25" height="36.75" align-x="469.5" align-y="4368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="130"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, а N2 - наименьшее целое число, большее или равное<sp count="2"/> </inlineAttr> </f> <region region-id="874" left="332.25" top="4383.75" width="65.25" height="36.75" align-x="380.25" align-y="4405.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="131"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> </text> </region> <region region-id="953" left="42" top="4434.75" width="319.5" height="13.5" align-x="42" align-y="4446" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Сформируем логический программный блок вычисления К</f> </text> </region> <region region-id="875" left="24" top="4476" width="237" height="80.25" align-x="41.25" align-y="4488" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">K</ml:id> <ml:program> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:lessThan/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N2</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:lessOrEqual/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:id xml:space="preserve">ε</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">N1</ml:id> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:lessThan/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N2</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:lessOrEqual/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N2</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:id xml:space="preserve">ε</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">N2</ml:id> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:ifThen> <ml:otherwise> <ml:real>0</ml:real> </ml:otherwise> </ml:program> </ml:define> </math> <rendering item-idref="132"/> </region> <region region-id="888" left="36" top="4578.75" width="321.75" height="13.5" align-x="36" align-y="4590" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Проверка и вывод на экран монитора численных значений:</f> </text> </region> <region region-id="893" left="378" top="4578.75" width="38.25" height="15.75" align-x="394.5" align-y="4590" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">K</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="133"/> </region> <region region-id="971" left="36" top="4602" width="419.25" height="33" align-x="36" align-y="4614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Если </f> <region region-id="904" left="65.25" top="4602.75" width="31.5" height="15.75" align-x="81.75" align-y="4614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:id xml:space="preserve">K</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="134"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, то номер n=K соответствует действительным равным корням,</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">в противном случае </f> <f family="Arial Cyr" charset="204" size="12">корни p1</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">, p2</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>действительные разные.</f> </text> </region> <region region-id="720" left="36" top="4649.25" width="469.5" height="44.25" align-x="36" align-y="4662" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Здесь и далее логическое равенство<sp count="2"/> </f> <region region-id="721" left="245.25" top="4650.75" width="40.5" height="15.75" align-x="267.75" align-y="4662" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </math> <rendering item-idref="135"/> </region> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>заменено неравенством </f> <region region-id="722" left="429.75" top="4650" width="60.75" height="16.5" align-x="474" align-y="4662" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessOrEqual/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:id xml:space="preserve">ε</ml:id> </ml:apply> </math> <rendering item-idref="136"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">так как практически невозможно задать N<sp count="2"/>как целое число. Н</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">еравенство</f> <f family="Arial Cyr" charset="204" size="12"> же </f> <f family="Arial Cyr" charset="204" size="12">позволяет </f> <f family="Arial Cyr" charset="204" size="12">искусственно создать в алгоритме эту ситуацию целого числа N.</f> </text> </region> <region region-id="954" left="36" top="4704.75" width="332.25" height="16.5" align-x="36" align-y="4716" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Теперь можно приступить к вычислению коэффициентов В</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">: </f> </text> </region> <region region-id="946" left="36" top="4734.75" width="139.5" height="15.75" align-x="62.25" align-y="4746" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">KK</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">N1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="137"/> </region> <region region-id="947" left="198" top="4734.75" width="47.25" height="15.75" align-x="223.5" align-y="4746" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">KK</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="138"/> </region> <region region-id="892" left="48" top="4770.75" width="57.75" height="15.75" align-x="61.5" align-y="4782" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">n</ml:id> <ml:range> <ml:real>1</ml:real> <ml:id xml:space="preserve">KK</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="139"/> </region> <region region-id="891" left="204" top="4767.75" width="283.5" height="57.75" align-x="225" align-y="4788" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:program> <ml:ifThen> <ml:apply> <ml:or/> <ml:parens> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">K</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:lessThan/> <ml:apply> <ml:lessOrEqual/> <ml:real>1</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">ν</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:ifThen> <ml:otherwise> <ml:real>0</ml:real> </ml:otherwise> </ml:program> </ml:define> </math> <rendering item-idref="140"/> </region> <region region-id="753" left="36" top="4848.75" width="321.75" height="13.5" align-x="36" align-y="4860" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Проверка и вывод на экран монитора численных значений:</f> </text> </region> <region region-id="980" left="54" top="4878.75" width="42" height="17.25" align-x="74.25" align-y="4890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="141"/> </region> <region region-id="979" left="132" top="4878.75" width="57" height="17.25" align-x="152.25" align-y="4890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:real>1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.4702103877914459</ml:real> </result> </ml:eval> </math> <rendering item-idref="142"/> </region> <region region-id="978" left="222" top="4878.75" width="41.25" height="17.25" align-x="242.25" align-y="4890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="index out of bounds" optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:eval> </math> <rendering item-idref="143"/> </region> <region region-id="977" left="330" top="4878.75" width="41.25" height="17.25" align-x="350.25" align-y="4890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="index out of bounds" optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:eval> </math> <rendering item-idref="144"/> </region> <region region-id="487" left="36" top="4950" width="480" height="60.75" align-x="36" align-y="4962" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10"> Примечание. </f> <f family="Arial Cyr" charset="204" size="10"> Если условия </f> <region region-id="488" left="162.75" top="4950.75" width="132.75" height="15.75" align-x="210" align-y="4962" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:or/> <ml:parens> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">K</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:lessThan/> <ml:apply> <ml:lessOrEqual/> <ml:real>1</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </ml:parens> </ml:apply> </math> <rendering item-idref="145"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> не выполнены, то B</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">можно не вычислять </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">или приравнять любой константе, в т. ч. нулю, т. к. формула решения будет другой. Поэтому опцию n=1..K-1 верную при</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="938" left="132" top="4983" width="32.25" height="15.75" align-x="148.5" align-y="4994.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">K</ml:id> <ml:real>2</ml:real> </ml:apply> </math> <rendering item-idref="146"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> и дающую сбой при K=0 следует заменить на n=1..KK, где KK=if(</inlineAttr> </f> <region region-id="965" left="467.25" top="4983" width="32.25" height="15.75" align-x="483.75" align-y="4994.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="147"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="10">, K-1, N1</f> </inlineAttr> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> ). </inlineAttr> </f> </text> </region> <region region-id="387" left="48" top="5028" width="249.75" height="20.25" align-x="48" align-y="5040" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> 2а)<sp count="2"/>Для </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="392" left="96.75" top="5028.75" width="30.75" height="15.75" align-x="109.5" align-y="5040" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterThan/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </math> <rendering item-idref="148"/> </region> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">(корни </f> <f family="Arial Cyr" charset="204" size="12">p1</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">, p2</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12"> комплексные)</f> </text> </region> <region region-id="900" left="48" top="5064.75" width="129.75" height="15.75" align-x="61.5" align-y="5076" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">n</ml:id> <ml:range> <ml:apply> <ml:id xml:space="preserve">max</ml:id> <ml:sequence> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">N2</ml:id> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">NN</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="149"/> </region> <region region-id="899" left="204" top="5055.75" width="110.25" height="36.75" align-x="225" align-y="5076" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">ν</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="150"/> </region> <region region-id="735" left="42" top="5106.75" width="321.75" height="13.5" align-x="42" align-y="5118" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Проверка и вывод на экран монитора численных значений:</f> </text> </region> <region region-id="901" left="378" top="5106.75" width="57.75" height="15.75" align-x="414" align-y="5118" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="151"/> </region> <region region-id="902" left="456" top="5106.75" width="44.25" height="15.75" align-x="478.5" align-y="5118" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N2</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>2</ml:real> </result> </ml:eval> </math> <rendering item-idref="152"/> </region> <region region-id="746" left="36" top="5142.75" width="65.25" height="17.25" align-x="64.5" align-y="5154" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.37960668982249446</ml:real> </result> </ml:eval> </math> <rendering item-idref="153"/> </region> <region region-id="747" left="108" top="5142.75" width="82.5" height="17.25" align-x="147.75" align-y="5154" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">N2</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.11113745888685707</ml:real> </result> </ml:eval> </math> <rendering item-idref="154"/> </region> <region region-id="748" left="204" top="5142.75" width="82.5" height="17.25" align-x="243.75" align-y="5154" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">N2</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.054229527117499204</ml:real> </result> </ml:eval> </math> <rendering item-idref="155"/> </region> <region region-id="749" left="312" top="5142.75" width="30" height="13.5" align-x="312" align-y="5154" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">и т. д.</f> </text> </region> <region region-id="750" left="366" top="5137.5" width="105.75" height="22.5" align-x="391.5" align-y="5154" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:real>51</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.00024967929585565751</ml:real> </result> </ml:eval> </math> <rendering item-idref="156"/> </region> <region region-id="395" left="48" top="5178" width="432.75" height="20.25" align-x="48" align-y="5190" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> 3а)<sp count="2"/>Для </f> <region region-id="409" left="96.75" top="5178.75" width="30.75" height="15.75" align-x="109.5" align-y="5190" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </math> <rendering item-idref="157"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (если<sp count="2"/>N целое, корни p1</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, p2</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>действительные равные)</inlineAttr> </f> </text> </region> <region region-id="394" left="66" top="5211.75" width="165" height="56.25" align-x="88.5" align-y="5232" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">K</ml:id> </ml:apply> <ml:program> <ml:ifThen> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">K</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">ν</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">K</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:ifThen> <ml:otherwise> <ml:real>0</ml:real> </ml:otherwise> </ml:program> </ml:define> </math> <rendering item-idref="158"/> </region> <region region-id="758" left="36" top="5292.75" width="321.75" height="13.5" align-x="36" align-y="5304" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Проверка и вывод на экран монитора численных значений:</f> </text> </region> <region region-id="996" left="36" top="5322.75" width="38.25" height="15.75" align-x="52.5" align-y="5334" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">K</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="159"/> </region> <region region-id="995" left="90" top="5322.75" width="42" height="17.25" align-x="110.25" align-y="5334" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="160"/> </region> <region region-id="994" left="150" top="5322.75" width="43.5" height="17.25" align-x="171.75" align-y="5334" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">K</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="161"/> </region> <region region-id="993" left="216" top="5322.75" width="69.75" height="17.25" align-x="249" align-y="5334" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.4702103877914459</ml:real> </result> </ml:eval> </math> <rendering item-idref="162"/> </region> <region region-id="399" left="24" top="5363.25" width="474.75" height="123.75" align-x="24" align-y="5376" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">В общем же случае, когда </f> <region region-id="397" left="168" top="5364" width="74.25" height="16.5" align-x="210.75" align-y="5376" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">V</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="163"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">,<sp count="2"/> </inlineAttr> </f> <region region-id="398" left="252" top="5364" width="81.75" height="18" align-x="300" align-y="5376" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:apply> <ml:id xml:space="preserve">V'</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="164"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> , будем иметь ([20], Будак, стр.231)</inlineAttr> </f> <region region-id="400" left="24" top="5396.25" width="108.75" height="90.75" align-x="45" align-y="5444.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">L1</ml:id> </ml:bounds> </ml:apply> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">L1</ml:id> </ml:bounds> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="165"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>,<sp count="5"/> </inlineAttr> </f> <region region-id="402" left="157.5" top="5396.25" width="165.75" height="90.75" align-x="233.25" align-y="5444.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">ν</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">L1</ml:id> </ml:bounds> </ml:apply> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">L1</ml:id> </ml:bounds> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="166"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> . Где L1<sp count="2"/>заданный отрезок.</inlineAttr> </f> </text> </region> <region region-id="765" left="24" top="5514.75" width="419.25" height="72.75" align-x="24" align-y="5526" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Проверка </f> <f family="Arial Cyr" charset="204" size="12">. V1</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12"> определяется как коэффициент ряда Фурье: </f> <region region-id="774" left="24" top="5532" width="214.5" height="55.5" align-x="51" align-y="5561.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">V1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">V0</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:apply> <ml:mult style="default"/> <ml:real>-2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:bounds> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="167"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, где 2L норма, равная </inlineAttr> </f> <region region-id="775" left="366" top="5535" width="73.5" height="44.25" align-x="410.25" align-y="5561.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:apply> <ml:mult style="auto-select"/> <ml:real>-2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:bounds> </ml:apply> </math> <rendering item-idref="168"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="791" left="24" top="5664.75" width="94.5" height="13.5" align-x="24" align-y="5676" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Вычислим норму:</f> </text> </region> <region region-id="790" left="138" top="5641.5" width="180.75" height="60.75" align-x="290.25" align-y="5676" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:real>13</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">U</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:apply> <ml:mult style="default"/> <ml:real>-2</ml:real> <ml:id xml:space="preserve">U</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">U</ml:id> </ml:apply> </ml:bounds> </ml:apply> <ml:symResult> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">U</ml:id> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="169"/> </region> <region region-id="789" left="348" top="5664" width="53.25" height="16.5" align-x="372.75" align-y="5676" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:symResult> <ml:apply> <ml:mult style="default"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="170"/> </region> <region region-id="792" left="426" top="5664.75" width="27" height="13.5" align-x="426" align-y="5676" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">ч.т.д.</f> </text> </region> <region region-id="817" left="18" top="5742.75" width="152.25" height="13.5" align-x="18" align-y="5754" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Проверка ортогональности:</f> </text> </region> <region region-id="818" left="186" top="5724.75" width="241.5" height="55.5" align-x="411" align-y="5754" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:real>1</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:apply> <ml:mult style="auto-select"/> <ml:real>-2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:bounds> </ml:apply> <ml:symResult> <ml:real>0</ml:real> </ml:symResult> </ml:symEval> </math> <rendering item-idref="171"/> </region> <region region-id="794" left="246" top="5802.75" width="207" height="55.5" align-x="421.5" align-y="5832" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">V0</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:real>3</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:bounds> </ml:apply> </ml:apply> <ml:symResult> <ml:apply> <ml:div/> <ml:real>4</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>5</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="172"/> </region> <region region-id="795" left="24" top="5826.75" width="202.5" height="13.5" align-x="24" align-y="5838" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Вычислим коэффициент ряда Фурье:</f> </text> </region> <region region-id="1109" left="24" top="5868.75" width="482.25" height="16.5" align-x="24" align-y="5880" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">С другой стороны V1</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">=A</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">. Далее нетрудно убедиться в справедливости общих формул. </f> </text> </region> <region region-id="819" left="24" top="5910.75" width="201.75" height="13.5" align-x="24" align-y="5922" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Вывод на экран численных значений:</f> </text> </region> <region region-id="820" left="252" top="5902.5" width="53.25" height="34.5" align-x="273.75" align-y="5922" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:symResult> <ml:apply> <ml:div/> <ml:real>4</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>5</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="173"/> </region> <region region-id="821" left="36" top="5946.75" width="90" height="13.5" align-x="36" align-y="5958" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Конец проверки.</f> </text> </region> <region region-id="1100" left="30" top="5976.75" width="482.25" height="57" align-x="30" align-y="5988" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Решение задачи (1) - (2) имеет переменную структуру, зависимую от<sp count="2"/>констант </f> <f family="Arial Cyr" charset="204" size="12">K, N1, N2, разбивающих множество индексов n на подмножества. Каждому набору подмножеств индексов n соответствует своя формула решения с коэффициентами </f> <f family="Arial Cyr" charset="204" size="12">B</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">.</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="935" left="36" top="6042.75" width="476.25" height="13.5" align-x="36" align-y="6054" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Выпишем четыре формулы вычисления решения и пятую V6(x,t) </f> <f family="Arial Cyr" charset="204" size="12">:</f> </text> </region> <region region-id="917" left="42" top="6072" width="417" height="30" align-x="42" align-y="6084" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">1. Решение для К=0 и<sp count="2"/> </f> <region region-id="918" left="164.25" top="6072.75" width="93.75" height="15.75" align-x="234" align-y="6084" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessThan/> <ml:apply> <ml:lessThan/> <ml:apply> <ml:lessOrEqual/> <ml:real>1</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="174"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> . Корни действительные разные и комплексные.</inlineAttr> </f> </text> </region> <region region-id="423" left="48" top="6117.75" width="399.75" height="99" align-x="94.5" align-y="6144" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V1</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:bounds> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">NN</ml:id> </ml:bounds> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="175"/> </region> <region region-id="919" left="42" top="6240" width="391.5" height="30" align-x="42" align-y="6252" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">2. Решение для<sp count="2"/> </f> <region region-id="923" left="132" top="6240.75" width="32.25" height="15.75" align-x="148.5" align-y="6252" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">K</ml:id> <ml:real>2</ml:real> </ml:apply> </math> <rendering item-idref="176"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> .</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">Корни действительные разные, комплексные</f> <f family="Arial Cyr" charset="204" size="12">и </f> <f family="Arial Cyr" charset="204" size="12">действительные равные</f> <f family="Arial Cyr" charset="204" size="12">.</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="425" left="48" top="6351.75" width="393" height="131.25" align-x="94.5" align-y="6378" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V2</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:bounds> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">NN</ml:id> </ml:bounds> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">K</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">K</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">K</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="177"/> </region> <region region-id="926" left="60" top="6492.75" width="423" height="13.5" align-x="60" align-y="6504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">3. Решение для К=1. </f> <f family="Arial Cyr" charset="204" size="12">Корни<sp count="2"/>комплексные и </f> <f family="Arial Cyr" charset="204" size="12">действительные равные</f> <f family="Arial Cyr" charset="204" size="12">.</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="426" left="54" top="6525.75" width="379.5" height="82.5" align-x="100.5" align-y="6552" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V3</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>2</ml:real> <ml:id xml:space="preserve">NN</ml:id> </ml:bounds> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="178"/> </region> <region region-id="929" left="60" top="6624.75" width="240.75" height="13.5" align-x="60" align-y="6636" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">4. Решение для N1=0 . </f> <f family="Arial Cyr" charset="204" size="12">Корни<sp count="2"/>комплексные.</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="429" left="48" top="6657.75" width="366" height="50.25" align-x="94.5" align-y="6684" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V4</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">NN</ml:id> </ml:bounds> </ml:apply> </ml:define> </math> <rendering item-idref="179"/> </region> <region region-id="554" left="48" top="6718.5" width="438" height="83.25" align-x="48" align-y="6744" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Поледнее выражение, получаемое при </f> <region region-id="930" left="263.25" top="6719.25" width="61.5" height="45" align-x="275.25" align-y="6744" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterThan/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="180"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">,</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>можно преобразовать к виду, если ввести</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="558" left="147" top="6765" width="71.25" height="36.75" align-x="192.75" align-y="6786" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">cot</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="181"/> </region> <f family="Arial Cyr" charset="204" size="12"> :</f> </text> </region> <region region-id="563" left="102" top="6828.75" width="87" height="15.75" align-x="116.25" align-y="6840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">NN</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="182"/> </region> <region region-id="564" left="222" top="6819.75" width="82.5" height="36.75" align-x="243" align-y="6840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">acot</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ν</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="183"/> </region> <region region-id="568" left="348" top="6819.75" width="63" height="34.5" align-x="390" align-y="6840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessOrEqual/> <ml:apply> <ml:lessThan/> <ml:real>0</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="184"/> </region> <region region-id="562" left="54" top="6873.75" width="406.5" height="50.25" align-x="100.5" align-y="6900" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V5</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">NN</ml:id> </ml:bounds> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="185"/> </region> <region region-id="1045" left="36" top="6953.25" width="357" height="29.25" align-x="36" align-y="6966" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">5. Решение для К-> </f> <region region-id="1047" left="143.25" top="6954" width="9.75" height="16.5" align-x="147" align-y="6966" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="186"/> </region> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>и<sp count="2"/> </f> <region region-id="1048" left="171.75" top="6954.75" width="15.75" height="15.75" align-x="178.5" align-y="6966" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">N1</ml:id> </math> <rendering item-idref="187"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">-></inlineAttr> </f> <region region-id="1049" left="198.75" top="6954" width="9.75" height="16.5" align-x="202.5" align-y="6966" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="188"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>. Корни действительные разные </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(В</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> этом файле эта формула не работает. См. "ВолнУр123_Алгоритм").</inlineAttr> </f> </text> </region> <region region-id="1046" left="42" top="7041.75" width="379.5" height="50.25" align-x="88.5" align-y="7068" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V6</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:bounds> </ml:apply> </ml:define> </math> <rendering item-idref="189"/> </region> <region region-id="968" left="42" top="7104.75" width="396.75" height="30" align-x="42" align-y="7116" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Вывод на экран монитора численных значений параметров, по которым </f> <f family="Arial Cyr" charset="204" size="12">выбирается одна из четырёх формул: </f> <region region-id="969" left="252.75" top="7119" width="38.25" height="15.75" align-x="269.25" align-y="7130.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">K</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="190"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">,<sp count="2"/> </inlineAttr> </f> <region region-id="970" left="300.75" top="7119" width="44.25" height="15.75" align-x="323.25" align-y="7130.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N1</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="191"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, </inlineAttr> </f> <region region-id="1007" left="351.75" top="7119" width="44.25" height="15.75" align-x="374.25" align-y="7130.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N2</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>2</ml:real> </result> </ml:eval> </math> <rendering item-idref="192"/> </region> </text> </region> <region region-id="571" left="54" top="7146.75" width="282" height="13.5" align-x="54" align-y="7158" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Логический блок выбора одной из четырех формул:</f> </text> </region> <region region-id="413" left="42" top="7182.75" width="202.5" height="100.5" align-x="82.5" align-y="7194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">K</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">V1</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">K</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">V2</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">V3</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">V5</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">∞</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">V6</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:ifThen> </ml:program> </ml:define> </math> <rendering item-idref="193"/> </region> <region region-id="1004" left="288" top="7182.75" width="162" height="100.5" align-x="303" align-y="7194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">fr</ml:id> <ml:program> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">K</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:str xml:space="preserve">V1</ml:str> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">K</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:str xml:space="preserve">V2</ml:str> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:str xml:space="preserve">V3</ml:str> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:str xml:space="preserve">V5</ml:str> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">∞</ml:id> </ml:apply> <ml:str xml:space="preserve">V6</ml:str> </ml:ifThen> </ml:program> </ml:define> </math> <rendering item-idref="194"/> </region> <region region-id="550" left="480" top="7188.75" width="21.75" height="15.75" align-x="489.75" align-y="7200" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>15</ml:real> </ml:parens> </math> <rendering item-idref="195"/> </region> <region region-id="1005" left="54" top="7314" width="407.25" height="16.5" align-x="54" align-y="7326" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Выбрана формула решения: </f> <region region-id="1006" left="213" top="7314.75" width="53.25" height="15.75" align-x="227.25" align-y="7326" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">fr</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">V1</ml:str> </result> </ml:eval> </math> <rendering item-idref="196"/> </region> </text> </region> <region region-id="1008" left="48" top="7334.25" width="444.75" height="24" align-x="48" align-y="7344" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">Можно дать следующее описание подмножеств множества индексов n, эквивалентное приведён-</f> <f family="Arial Cyr" charset="204" size="10">ному в (15), если положить </f> <f family="Symbol" charset="2" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">e</inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">=0 </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Описание приводится в той же последовательности, что и в (15).</inlineAttr> </f> </text> </region> <region region-id="1009" left="48" top="7368" width="435.75" height="37.5" align-x="48" align-y="7380" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">1. Выбор параметров: </f> <region region-id="1010" left="150" top="7368.75" width="46.5" height="15.75" align-x="172.5" align-y="7380" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="197"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> and </inlineAttr> </f> <region region-id="1011" left="219" top="7368.75" width="38.25" height="15.75" align-x="241.5" align-y="7380" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="198"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> приводит к разбиению на подмножества:</inlineAttr> </f> <region region-id="1012" left="48" top="7386" width="48.75" height="15.75" align-x="60.75" align-y="7397.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1..</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="199"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(корни </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10">p1</f> <f family="Arial Cyr" charset="204" size="10"> n </f> <f family="Arial Cyr" charset="204" size="10">, p2</f> <f family="Arial Cyr" charset="204" size="10"> n </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> действительные разные), </inlineAttr> </f> <region region-id="1013" left="288" top="7386" width="36.75" height="15.75" align-x="300.75" align-y="7397.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="200"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">..</inlineAttr> </f> <region region-id="1014" left="331.5" top="7385.25" width="9.75" height="16.5" align-x="335.25" align-y="7397.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="201"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> комплексные).</inlineAttr> </f> </text> </region> <region region-id="1015" left="48" top="7416" width="447.75" height="57.75" align-x="48" align-y="7428" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">2. Выбор параметров: </f> <region region-id="1017" left="150" top="7416.75" width="46.5" height="15.75" align-x="172.5" align-y="7428" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="202"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> and </inlineAttr> </f> <region region-id="1018" left="219" top="7416.75" width="38.25" height="15.75" align-x="241.5" align-y="7428" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>2</ml:real> </ml:apply> </math> <rendering item-idref="203"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> приводит к разбиению на подмножества:</inlineAttr> </f> <region region-id="1019" left="48" top="7433.25" width="67.5" height="15.75" align-x="60.75" align-y="7444.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1..</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="204"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204">n</f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="10"> действительные разные), </f> </inlineAttr> <region region-id="1016" left="306.75" top="7433.25" width="36.75" height="15.75" align-x="319.5" align-y="7444.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> </math> <rendering item-idref="205"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="10"> <sp/> </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(</inlineAttr> </f> <f family="Arial Cyr" charset="204">корни </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204"> действительные равные),</f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="10"> <sp/> </f> </inlineAttr> <region region-id="1020" left="90" top="7454.25" width="56.25" height="15.75" align-x="102.75" align-y="7465.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="206"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">..</inlineAttr> </f> <region region-id="1021" left="153" top="7453.5" width="9.75" height="16.5" align-x="156.75" align-y="7465.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="207"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204">n</f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="10"> комплексные).</f> </inlineAttr> </text> </region> <region region-id="1023" left="48" top="7488" width="406.5" height="37.5" align-x="48" align-y="7500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">3. Выбор параметров: </f> <region region-id="1026" left="150" top="7488.75" width="46.5" height="15.75" align-x="172.5" align-y="7500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="208"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> and </inlineAttr> </f> <region region-id="1027" left="219" top="7488.75" width="37.5" height="15.75" align-x="241.5" align-y="7500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="209"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> приводит к разбиению на подмножества:</inlineAttr> </f> <region region-id="1028" left="48" top="7506" width="27.75" height="15.75" align-x="60.75" align-y="7517.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="210"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> действительные равные), </inlineAttr> </f> <region region-id="1029" left="267.75" top="7506" width="27.75" height="15.75" align-x="280.5" align-y="7517.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:real>2</ml:real> </ml:apply> </math> <rendering item-idref="211"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">..</inlineAttr> </f> <region region-id="1030" left="302.25" top="7505.25" width="9.75" height="16.5" align-x="306" align-y="7517.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="212"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> комплексные).</inlineAttr> </f> </text> </region> <region region-id="1025" left="48" top="7535.25" width="451.5" height="33" align-x="48" align-y="7548" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">4. Выбор параметров: </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="1032" left="153" top="7536.75" width="37.5" height="15.75" align-x="175.5" align-y="7548" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="213"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> приводит к разбиению на подмножества:</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="1034" left="382.5" top="7536.75" width="27.75" height="15.75" align-x="395.25" align-y="7548" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="214"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">..</inlineAttr> </f> <region region-id="1035" left="417" top="7536" width="9.75" height="16.5" align-x="420.75" align-y="7548" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="215"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204">n</f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> комплексные).</inlineAttr> </f> </text> </region> <region region-id="1040" left="48" top="7577.25" width="331.5" height="37.5" align-x="48" align-y="7590" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204">5. Выбор параметров:</f> <f family="Arial Cyr" charset="204"> <sp/> </f> <region region-id="1041" left="150" top="7578.75" width="15.75" height="15.75" align-x="156.75" align-y="7590" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">N1</ml:id> </math> <rendering item-idref="216"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">-></inlineAttr> </f> <region region-id="1042" left="175.5" top="7578" width="9.75" height="16.5" align-x="179.25" align-y="7590" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="217"/> </region> <f family="Arial Cyr" charset="204"> <sp count="2"/>приводит к разбиению на подмножества:</f> <region region-id="1037" left="48" top="7595.25" width="48.75" height="15.75" align-x="60.75" align-y="7606.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1..</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="218"/> </region> <f family="Arial Cyr" charset="204"> <sp/> </f> <f family="Arial Cyr" charset="204">(корни </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204"> действительные разные)</f> </text> </region> <region region-id="1110" left="42" top="7644.75" width="198" height="13.5" align-x="42" align-y="7656" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Возможна анимация по параметру t:</f> </text> </region> <region region-id="1111" left="276" top="7636.5" width="80.25" height="33.75" align-x="287.25" align-y="7656" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">t</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>10</ml:real> </ml:apply> <ml:id xml:space="preserve">FRAME</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="219"/> </region> <region region-id="1112" left="390" top="7644.75" width="92.25" height="15.75" align-x="439.5" align-y="7656" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">V</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>10</ml:real> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.17258531028748556</ml:real> </result> </ml:eval> </math> <rendering item-idref="220"/> </region> <region region-id="236" left="54" top="7740" width="381.75" height="175.5" align-x="54" align-y="7740" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="221"/> <rendering item-idref="222"/> </region> <region region-id="68" left="48" top="7944" width="429.75" height="14.25" align-x="48" 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size="12"> <inlineAttr underline="false">2) Уменьшение R сильно увеличивает колебательность процесса и наоборот - увеличение R уменьшает колебательность.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr underline="false">3) Увеличение самоиндукции J замедляет процесс и уменьшает колебательность.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr underline="false">4) Ситуация n=N - целое число (<sp count="2"/> </inlineAttr> </f> <region region-id="937" left="244.5" top="8548.5" width="32.25" height="15.75" align-x="261" align-y="8559.75" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">N</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="234"/> </region> <f family="Arial Cyr" charset="204" size="12"> 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size="12"> <inlineAttr font-weight="normal"> <c val="#000"> Пример решения, имеющего переменную структуру. </c> </inlineAttr> </f> <f family="Times New Roman" charset="204" size="12"> <inlineAttr font-weight="normal"> <c val="#000">(</c> </inlineAttr> </f> <f family="Times New Roman Cyr" charset="204" size="12">Решение уравнений в частных производных</f> <f family="Arial Cyr" charset="204" size="12">)</f> </text> </region> <region region-id="2" left="30" top="48.75" width="456" height="119.25" align-x="30" align-y="60" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Уравнение, описывающее динамику </f> <f family="Arial Cyr" charset="204" size="12">изменения тока или напряжения в проводах,</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="5"/>представляемую<sp count="2"/>функцией "v(х,t)" переменных<sp count="2"/>"x" и "t".</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12">Для линейного дифференциального ур-я 2-го порядка в частных производных в случае двух независимых переменных, тип уравнения определяется по коэффициентам при вторых производных. Если Д>0 - гиперболичкский, Д<0 -<sp count="3"/>эллиптический, Д=0 - параболический тип.(где Д=А</f> <f family="Arial Cyr" charset="204" size="12"> 12 </f> <f family="Arial Cyr" charset="204" size="12">-А</f> <f family="Arial Cyr" charset="204" size="12"> 11 </f> <f family="Arial Cyr" charset="204" size="12">*А</f> <f family="Arial Cyr" charset="204" size="12"> 22 </f> <f family="Arial Cyr" charset="204" size="12">, а само уравнение выглядит так: </f> <region region-id="61" left="107.25" top="133.5" width="255.75" height="20.25" align-x="348" align-y="144.75" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="11">A</ml:id> <ml:id xml:space="preserve" subscript="tt">v</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="12">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="xt">v</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="22">A</ml:id> <ml:id xml:space="preserve" subscript="xx">v</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">v</ml:id> <ml:id xml:space="preserve" subscript="t">v</ml:id> <ml:id xml:space="preserve" subscript="x">v</ml:id> </ml:sequence> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="2"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> ).</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" line-through="false"> А) Решение методом Фурье (разделения переменных).</inlineAttr> </f> </text> </region> <region region-id="70" left="30" top="180.75" width="375.75" height="13.5" align-x="30" align-y="192" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Постановка задачи (№123) и её</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal">словесное описание [20]:</inlineAttr> </f> </text> </region> <region region-id="611" left="30" top="204" width="445.5" height="70.5" align-x="30" align-y="216" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> изолированный однородный электрический провод </f> <region region-id="244" left="314.25" top="204.75" width="51.75" height="15.75" align-x="349.5" align-y="216" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessOrEqual/> <ml:apply> <ml:lessOrEqual/> <ml:real>0</ml:real> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </math> <rendering item-idref="3"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> заряжен до некоторого потенциала V0=const. В начальный момент времени конец<sp count="2"/>х=0<sp count="2"/>заземляется, а конец<sp count="2"/>x=L<sp count="2"/>продолжает оставаться изолированным. Найти распределение напряжения в проводе, если самоиндукция, сопротивление и емкость единицы длины известны.</inlineAttr> </f> </text> </region> <region region-id="612" left="30" top="288.75" width="119.25" height="13.5" align-x="30" align-y="300" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Задание параметров. </f> </text> </region> <region region-id="599" left="30" top="312" width="151.5" height="14.25" align-x="30" align-y="324" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Независимые параметры: </f> </text> </region> <region region-id="603" left="30" top="335.25" width="432.75" height="50.25" align-x="30" align-y="348" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Самоиндукция: </f> <region region-id="604" left="115.5" top="336.75" width="29.25" height="15.75" align-x="128.25" align-y="348" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">J</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="4"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">; сопротивление: </inlineAttr> </f> <region region-id="605" left="242.25" top="336.75" width="32.25" height="15.75" align-x="258" align-y="348" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">R</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="5"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">;<sp count="2"/>длина провода: </f> </inlineAttr> <region region-id="606" left="377.25" top="336" width="43.5" height="16.5" align-x="392.25" align-y="348" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">L</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="6"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">;</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">время наблюдения процесса: </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="607" left="198.75" top="353.25" width="37.5" height="15.75" align-x="213.75" align-y="364.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">T</ml:id> <ml:real>15</ml:real> </ml:define> </math> <rendering item-idref="7"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">; начальнй потенциал провода: </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="608" left="33" top="369.75" width="39" height="15.75" align-x="55.5" align-y="381" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">V0</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="8"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">; </f> </inlineAttr> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">ёмкость провода: </f> </inlineAttr> <region region-id="830" left="182.25" top="369.75" width="30" height="15.75" align-x="195.75" align-y="381" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="9"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </inlineAttr> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>.</f> </inlineAttr> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </inlineAttr> </text> </region> <region region-id="952" left="30" top="396" width="82.5" height="14.25" align-x="30" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Обозначения: </f> </text> </region> <region region-id="1098" left="132" top="396.75" width="37.5" height="15.75" align-x="145.5" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="1099" left="186" top="396.75" width="41.25" height="15.75" align-x="200.25" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="843" left="30" top="424.5" width="479.25" height="59.25" align-x="30" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Критерий выбора параметров: 1) если </f> <region region-id="846" left="243" top="425.25" width="63" height="45" align-x="255" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterThan/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="12"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> , то корни комплексные для всех n</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(N<1) и<sp count="2"/>получаем решение V4(x,t)<sp count="2"/>(</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">V5(x,t)</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">). При этом kr=5.</inlineAttr> </f> </text> </region> <region region-id="844" left="30" top="497.25" width="135.75" height="45" align-x="48" align-y="522" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">kr</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:real>5</ml:real> <ml:real>0</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="845" left="204" top="510.75" width="39" height="15.75" align-x="221.25" align-y="522" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">kr</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="14"/> </region> <region region-id="613" left="36" top="552.75" width="384.75" height="13.5" align-x="36" align-y="564" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Математическая модель. </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="10">(Вывод см. в лекциях или у Пискунова, т.2, стр.367.) </f> </text> </region> <region region-id="72" left="42" top="582.75" width="111.75" height="20.25" align-x="68.25" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve" subscript="xx">V</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="tt">V</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t">V</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="15"/> </region> <region region-id="92" left="216" top="582.75" width="51.75" height="15.75" align-x="251.25" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessOrEqual/> <ml:apply> <ml:lessOrEqual/> <ml:real>0</ml:real> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </math> <rendering item-idref="16"/> </region> <region region-id="93" left="312" top="582.75" width="25.5" height="15.75" align-x="322.5" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterThan/> <ml:id xml:space="preserve">t</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="17"/> </region> <region region-id="130" left="474" top="582.75" width="15.75" height="15.75" align-x="480.75" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </ml:parens> </math> <rendering item-idref="18"/> </region> <region region-id="615" left="30" top="612.75" width="450.75" height="46.5" align-x="30" align-y="624" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Здесь: V(x,t) - напряжение в сечении провода с координатой х в момент времени t;</f> <f family="Arial Cyr" charset="204" size="12">A</f> <f family="Arial Cyr" charset="204" size="12"> 12 </f> <f family="Arial Cyr" charset="204" size="12">=0; </f> <f family="Arial Cyr" charset="204" size="12">A</f> <f family="Arial Cyr" charset="204" size="12"> 11 </f> <f family="Arial Cyr" charset="204" size="12">=-c*J; </f> <f family="Arial Cyr" charset="204" size="12">A2</f> <f family="Arial Cyr" charset="204" size="12"> 2 </f> <f family="Arial Cyr" charset="204" size="12"> 2 </f> <f family="Arial Cyr" charset="204" size="12">=1.<sp count="2"/>Поэтому (Д=c*J>0)<sp count="2"/>уравнение (1) имеет гиперболический</f> <f family="Arial Cyr" charset="204" size="12">тип. V</f> <f family="Arial Cyr" charset="204" size="12"> xx </f> <f family="Arial Cyr" charset="204" size="12"> - </f> <f family="Arial Cyr" charset="204" size="12">вторая </f> <f family="Arial Cyr" charset="204" size="12">частная производная по х, V</f> <f family="Arial Cyr" charset="204" size="12"> tt </f> <f family="Arial Cyr" charset="204" size="12"> - тоже по t, и т. д.</f> </text> </region> <region region-id="99" left="42" top="672" width="204.75" height="14.25" align-x="42" align-y="684" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Краевые условия: </f> </text> </region> <region region-id="100" left="42" top="708.75" width="66" height="15.75" align-x="84.75" align-y="720" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">V</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> </math> <rendering item-idref="19"/> </region> <region region-id="107" left="132" top="708.75" width="60.75" height="20.25" align-x="177.75" align-y="720" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="t">V</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:sequence> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="20"/> </region> <region region-id="108" left="216" top="708.75" width="108.75" height="13.5" align-x="216" align-y="720" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Начальные условия</f> </text> </region> <region region-id="1113" left="474" top="738.75" width="15.75" height="15.75" align-x="480.75" align-y="750" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>2</ml:real> </ml:parens> </math> <rendering item-idref="21"/> </region> <region region-id="102" left="48" top="750.75" width="55.5" height="15.75" align-x="88.5" align-y="762" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">V</ml:id> <ml:sequence> <ml:real>0</ml:real> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="22"/> </region> <region region-id="103" left="120" top="750.75" width="61.5" height="20.25" align-x="166.5" align-y="762" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="x">V</ml:id> <ml:sequence> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="23"/> </region> <region region-id="110" left="216" top="750.75" width="106.5" height="13.5" align-x="216" align-y="762" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Граничные условия</f> </text> </region> <region region-id="114" left="42" top="786" width="129" height="14.25" align-x="42" align-y="798" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12"> Решение </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false"> ищем в виде:</inlineAttr> </f> </text> </region> <region region-id="617" left="204" top="786.75" width="95.25" height="15.75" align-x="243.75" align-y="798" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">V</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="24"/> </region> <region region-id="637" left="474" top="786.75" width="28.5" height="15.75" align-x="487.5" align-y="798" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">resh</ml:id> </ml:parens> </math> <rendering item-idref="25"/> </region> <region region-id="619" left="42" top="810.75" width="352.5" height="13.5" align-x="42" align-y="822" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Исходя из краевых условий (2), запишем следующие выражения:</f> </text> </region> <region region-id="631" left="54" top="834.75" width="80.25" height="15.75" align-x="75.75" align-y="846" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">V0</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="26"/> </region> <region region-id="632" left="156" top="834.75" width="74.25" height="15.75" align-x="169.5" align-y="846" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:real>0</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T'</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="27"/> </region> <region region-id="956" left="462" top="846.75" width="21" height="15.75" align-x="471.75" align-y="858" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:mult style="auto-select"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:parens> </math> <rendering item-idref="28"/> </region> <region region-id="1084" left="54" top="864.75" width="69.75" height="15.75" align-x="67.5" align-y="876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:real>0</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="29"/> </region> <region region-id="628" left="150" top="864.75" width="72.75" height="15.75" align-x="163.5" align-y="876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:real>0</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">X'</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="30"/> </region> <region region-id="1082" left="36" top="894" width="461.25" height="43.5" align-x="36" align-y="906" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Из этих равенств следует, что </f> <region region-id="635" left="202.5" top="894.75" width="45.75" height="15.75" align-x="233.25" align-y="906" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="31"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> и </inlineAttr> </f> <region region-id="636" left="261" top="894.75" width="42" height="15.75" align-x="288" align-y="906" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="32"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. В противном случае мы </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">получаем </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">тривиальное (нулевое) решение. Подстановка (resh) в (1) приводит </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">к двум линейным дифференциальным </f> </inlineAttr> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">уравнениям 2-го порядка:</f> </inlineAttr> </text> </region> <region region-id="649" left="42" top="960.75" width="76.5" height="13.5" align-x="42" align-y="972" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Первое из них</f> </text> </region> <region region-id="648" left="138" top="945.75" width="115.5" height="44.25" align-x="238.5" align-y="972" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="33"/> </region> <region region-id="653" left="462" top="966.75" width="15.75" height="15.75" align-x="468.75" align-y="978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>3</ml:real> </ml:parens> </math> <rendering item-idref="34"/> </region> <region region-id="650" left="42" top="1002.75" width="140.25" height="13.5" align-x="42" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">с начальными условиями:</f> </text> </region> <region region-id="652" left="198" top="1002.75" width="46.5" height="15.75" align-x="229.5" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="35"/> </region> <region region-id="651" left="276" top="1002.75" width="49.5" height="15.75" align-x="310.5" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">X'</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="36"/> </region> <region region-id="656" left="42" top="1029" width="476.25" height="70.5" align-x="42" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">позволяет найти </f> <region region-id="655" left="134.25" top="1038.75" width="53.25" height="17.25" align-x="165" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="37"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> ,<sp count="2"/>где<sp count="2"/> </inlineAttr> </f> <region region-id="657" left="224.25" top="1035.75" width="84" height="20.25" align-x="245.25" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:sqrt/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="38"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">,<sp count="3"/> </inlineAttr> </f> <region region-id="658" left="321" top="1029.75" width="96" height="34.5" align-x="350.25" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:sqrt/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="39"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/> </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">П</f> </inlineAttr> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">оследние </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12">называют:</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="661" left="165" top="1065" width="13.5" height="18" align-x="171" align-y="1077" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="40"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> -</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="3"/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">собственными значениями </f> <f family="Arial Cyr" charset="204" size="12"> и</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>соответствующие им </f> <f family="Arial Cyr" charset="204" size="12">Х</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">(x) - </f> <f family="Arial Cyr" charset="204" size="12">собственными функциями</f> <f family="Arial Cyr" charset="204" size="12">.</f> </text> </region> <region region-id="690" left="42" top="1110.75" width="441.75" height="43.5" align-x="42" align-y="1122" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Причём {X</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">} представляет систему ортогональных функций на отрезке [-2L,2L], а</f> <f family="Arial Cyr" charset="204" size="12">также на отрезках: </f> <f family="Arial Cyr" charset="204" size="12">[0,2L] или </f> <f family="Arial Cyr" charset="204" size="12">[-L,L], </f> <f family="Arial Cyr" charset="204" size="12">[0,L] или</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">[-L/2,L/2] (см. файл: "СистОртогФункций"\</f> <f family="Arial Cyr" charset="204" size="12">"СистОртогФункций.xmcd".</f> </text> </region> <region region-id="675" left="174" top="1173.75" width="101.25" height="34.5" align-x="223.5" align-y="1194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:parens> </math> <rendering item-idref="41"/> </region> <region region-id="676" left="300" top="1182.75" width="52.5" height="15.75" align-x="341.25" align-y="1194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:sequence xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:real>2</ml:real> <ml:id xml:space="preserve" font="1">...</ml:id> </ml:sequence> </math> <rendering item-idref="42"/> </region> <region region-id="677" left="456" top="1182.75" width="15.75" height="15.75" align-x="462.75" align-y="1194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>4</ml:real> </ml:parens> </math> <rendering item-idref="43"/> </region> <region region-id="1051" left="48" top="1224.75" width="344.25" height="13.5" align-x="48" align-y="1236" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Правда, для указанных выше отрезков, нормы будут разными: </f> </text> </region> <region region-id="1054" left="48" top="1254.75" width="314.25" height="61.5" align-x="71.25" align-y="1290" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">nor</ml:id> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:bounds> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">substitute</ml:id> <ml:apply> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </ml:sequence> </ml:command> <ml:command> <ml:id xml:space="preserve">simplify</ml:id> </ml:command> <ml:symResult> <ml:id xml:space="preserve">π</ml:id> </ml:symResult> </ml:symEval> </ml:define> </math> <rendering item-idref="44"/> </region> <region region-id="1067" left="432" top="1278.75" width="21" height="15.75" align-x="441.75" align-y="1290" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:mult style="auto-select"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:parens> </math> <rendering item-idref="45"/> </region> <region region-id="1068" left="438" top="1344.75" width="21.75" height="15.75" align-x="447.75" align-y="1356" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real base="2">4</ml:real> </ml:parens> </math> <rendering item-idref="46"/> </region> <region region-id="1057" left="48" top="1332.75" width="339" height="61.5" align-x="77.25" align-y="1368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">nor1</ml:id> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:bounds> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">substitute</ml:id> <ml:apply> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </ml:sequence> </ml:command> <ml:command> <ml:id xml:space="preserve">simplify</ml:id> </ml:command> <ml:symResult> <ml:apply> <ml:mult style="narrow-dot"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:symResult> </ml:symEval> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="1059" left="54" top="1416.75" width="329.25" height="13.5" align-x="54" align-y="1428" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Нас интересует отрезок [0,L] и соответствующая ему норма.</f> </text> </region> <region region-id="659" left="42" top="1457.25" width="462" height="18.75" align-x="42" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Второе из уравнений с учётом найденного значения </f> <region region-id="694" left="327" top="1458" width="13.5" height="18" align-x="333" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="48"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> будет иметь вид:</inlineAttr> </f> </text> </region> <region region-id="691" left="42" top="1485.75" width="184.5" height="44.25" align-x="211.5" align-y="1512" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="49"/> </region> <region region-id="692" left="264" top="1500.75" width="27.75" height="15.75" align-x="276.75" align-y="1512" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:id xml:space="preserve">a</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="50"/> </region> <region region-id="693" left="366" top="1500.75" width="15.75" height="15.75" align-x="372.75" align-y="1512" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>5</ml:real> </ml:parens> </math> <rendering item-idref="51"/> </region> <region region-id="151" left="36" top="1547.25" width="439.5" height="45.75" align-x="36" align-y="1560" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Находим решение (5) , которое будет зависеть от значения </f> <region region-id="159" left="361.5" top="1548" width="13.5" height="18" align-x="367.5" align-y="1560" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="52"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Для этого найдем корни характеристического уравнения, соответствующего уравнению (5).</inlineAttr> </f> </text> </region> <region region-id="252" left="48" top="1602" width="77.25" height="18" align-x="72.75" align-y="1614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="53"/> </region> <region region-id="253" left="174" top="1602" width="76.5" height="18" align-x="198.75" align-y="1614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p2</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="54"/> </region> <region region-id="254" left="294" top="1602.75" width="52.5" height="15.75" align-x="335.25" align-y="1614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:sequence xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:real>2</ml:real> <ml:id xml:space="preserve" font="1">...</ml:id> </ml:sequence> </math> <rendering item-idref="55"/> </region> <region region-id="273" left="480" top="1602.75" width="15.75" height="15.75" align-x="486.75" align-y="1614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>6</ml:real> </ml:parens> </math> <rendering item-idref="56"/> </region> <region region-id="291" left="42" top="1656.75" width="27" height="13.5" align-x="42" align-y="1668" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">где: </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="299" left="78" top="1648.5" width="43.5" height="33.75" align-x="93.75" align-y="1668" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ν</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">R</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="57"/> </region> <region region-id="304" left="144" top="1641" width="198" height="47.25" align-x="167.25" align-y="1668" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="58"/> </region> <region region-id="305" left="474" top="1656.75" width="15.75" height="15.75" align-x="480.75" align-y="1668" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>7</ml:real> </ml:parens> </math> <rendering item-idref="59"/> </region> <region region-id="695" left="30" top="1710.75" width="488.25" height="27" align-x="30" align-y="1722" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">В зависимости от выбора параметров и, что самое главное, от значений индекса "n", корни (6) могут быть как действительными разными или равными, так и комплексными. </f> </text> </region> <region region-id="268" left="24" top="1750.5" width="406.5" height="96.75" align-x="24" align-y="1776" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Поэтому найдем такое n, при котором </f> <region region-id="261" left="233.25" top="1751.25" width="117.75" height="45" align-x="336" align-y="1776" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="60"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Или </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="267" left="27" top="1797" width="86.25" height="36.75" align-x="39.75" align-y="1818.75" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">R</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="61"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> .</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Обозначим это значение через N</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="266" left="132" top="1862.25" width="92.25" height="36.75" align-x="149.25" align-y="1884" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">R</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="62"/> </region> <region region-id="577" left="264" top="1872.75" width="47.25" height="15.75" align-x="280.5" align-y="1884" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.5</ml:real> </result> </ml:eval> </math> <rendering item-idref="63"/> </region> <region region-id="696" left="486" top="1872.75" width="15.75" height="15.75" align-x="492.75" align-y="1884" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>8</ml:real> </ml:parens> </math> <rendering item-idref="64"/> </region> <region region-id="578" left="24" top="1922.25" width="466.5" height="12" align-x="24" align-y="1932" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">Примечание. Можно подогнать R так, чтобы N было целым. Для этого R будем вычислять по формуле:</f> </text> </region> <region region-id="579" left="36" top="1952.25" width="148.5" height="36" align-x="59.25" align-y="1974" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">RR</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">ceil</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">J</ml:id> <ml:id xml:space="preserve">c</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="65"/> </region> <region region-id="580" left="222" top="1962.75" width="53.25" height="15.75" align-x="244.5" align-y="1974" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">RR</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.5</ml:real> </result> </ml:eval> </math> <rendering item-idref="66"/> </region> <region region-id="581" left="30" top="2000.25" width="477" height="12" align-x="30" align-y="2010" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">Полученное значение R=RR надо подставить в исходные данные в начале листинга. Конец Примечания.</f> </text> </region> <region region-id="278" left="30" top="2034.75" width="423" height="27" align-x="30" align-y="2046" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Значения (8) приводят к разбиению множества индексов n<sp count="2"/>на подмножества.</f> <f family="Arial Cyr" charset="204" size="12">Учитывая (8), решение уравнения (5) запишется в следующем виде:</f> </text> </region> <region region-id="279" left="36" top="2130" width="343.5" height="20.25" align-x="36" align-y="2142" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> 1) Для </f> <region region-id="166" left="75" top="2130.75" width="30.75" height="15.75" align-x="87.75" align-y="2142" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessThan/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </math> <rendering item-idref="67"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (корни p1</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, p2</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>действительные разные)</inlineAttr> </f> </text> </region> <region region-id="309" left="36" top="2158.5" width="218.25" height="25.5" align-x="80.25" align-y="2178" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">T1</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="68"/> </region> <region region-id="311" left="282" top="2166.75" width="112.5" height="13.5" align-x="282" align-y="2178" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">или, что одно и тоже:</f> </text> </region> <region region-id="281" left="36" top="2196.75" width="246.75" height="23.25" align-x="80.25" align-y="2214" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">T1</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="69"/> </region> <region region-id="284" left="480" top="2202.75" width="15.75" height="15.75" align-x="486.75" align-y="2214" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>9</ml:real> </ml:parens> </math> <rendering item-idref="70"/> </region> <region region-id="316" left="36" top="2232" width="205.5" height="18" align-x="36" align-y="2244" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">где: </f> <region region-id="314" left="60" top="2232.75" width="81.75" height="17.25" align-x="81" align-y="2244" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="71"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> ,<sp count="2"/> </inlineAttr> </f> <region region-id="315" left="154.5" top="2232.75" width="80.25" height="17.25" align-x="174.75" align-y="2244" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="72"/> </region> </text> </region> <region region-id="180" left="42" top="2268" width="243" height="20.25" align-x="42" align-y="2280" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> 2) Для </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="197" left="81" top="2268.75" width="30.75" height="15.75" align-x="93.75" align-y="2280" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterThan/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </math> <rendering item-idref="73"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">(корни </f> <f family="Arial Cyr" charset="204" size="12">p1</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">, p2</f> <f family="Arial Cyr" charset="204" size="12">n</f> <f family="Arial Cyr" charset="204" size="12"> комплексные)</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="322" left="288" top="2253" width="196.5" height="47.25" align-x="309.75" align-y="2280" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="74"/> </region> <region region-id="286" left="48" top="2304.75" width="233.25" height="23.25" align-x="92.25" align-y="2322" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">T2</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="75"/> </region> <region region-id="287" left="480" top="2310.75" width="21.75" height="15.75" align-x="489.75" align-y="2322" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>10</ml:real> </ml:parens> </math> <rendering item-idref="76"/> </region> <region region-id="318" left="42" top="2340" width="432.75" height="33" align-x="42" align-y="2352" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> 3) Для </f> <region region-id="333" left="81" top="2340.75" width="30.75" height="15.75" align-x="93.75" align-y="2352" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </math> <rendering item-idref="77"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>(так как n по определению целое число, то в этом случае и<sp count="3"/>N<sp count="2"/>также целое, и корни p1</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, p2</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>действительные равные)</inlineAttr> </f> </text> </region> <region region-id="327" left="60" top="2388.75" width="140.25" height="23.25" align-x="104.25" align-y="2406" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">T3</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="78"/> </region> <region region-id="324" left="486" top="2394.75" width="21.75" height="15.75" align-x="495.75" align-y="2406" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>11</ml:real> </ml:parens> </math> <rendering item-idref="79"/> </region> <region region-id="1103" left="36" top="2426.25" width="398.25" height="56.25" align-x="36" align-y="2448" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">Примечание:<sp count="2"/> </f> <region region-id="1102" left="100.5" top="2427" width="236.25" height="36.75" align-x="156" align-y="2448" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">T3</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="80"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. При </inlineAttr> </f> <region region-id="1104" left="363.75" top="2436.75" width="25.5" height="15.75" align-x="374.25" align-y="2448" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">t</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="81"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> получим</inlineAttr> </f> <region region-id="1105" left="36" top="2464.5" width="80.25" height="18" align-x="101.25" align-y="2476.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="82"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="957" left="30" top="2502.75" width="444" height="64.5" align-x="30" align-y="2514" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Так как в каждом случае </f> <f family="Arial Cyr" charset="204" size="12"> 1), 2), 3) </f> <f family="Arial Cyr" charset="204" size="12"> индекы </f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12"> разные, то это даёт н</f> <f family="Arial Cyr" charset="204" size="12">ам </f> <f family="Arial Cyr" charset="204" size="12">возможность записывать в вектор</f> <f family="Arial Cyr" charset="204" size="12">, в общем случае различные,<sp count="2"/>коэффициенты </f> <region region-id="329" left="393.75" top="2517.75" width="14.25" height="17.25" align-x="399.75" align-y="2529" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="83"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">, </f> </inlineAttr> <region region-id="330" left="414.75" top="2517.75" width="13.5" height="17.25" align-x="420.75" align-y="2529" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="84"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>равно как и </f> </inlineAttr> <region region-id="331" left="59.25" top="2535.75" width="15" height="18" align-x="66" align-y="2547.75" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="85"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> , обозначение которых вместе с самой функцией T(t,n) можно оставить единым для всех трех случаев.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="698" left="30" top="2574.75" width="465.75" height="34.5" align-x="30" align-y="2586" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Подставим найденные X</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">(x)</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>и T</f> <f family="Arial Cyr" charset="204" size="12">(t,n) в (resh) и, используя начальные условия в (2), запишем два уравнения для </f> <f family="Arial Cyr" charset="204" size="12">определения к</f> <f family="Arial Cyr" charset="204" size="12">оэффициентов </f> <region region-id="335" left="351" top="2592" width="14.25" height="17.25" align-x="357" align-y="2603.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="86"/> </region> <f family="Arial Cyr" charset="204" size="12">, </f> <region region-id="336" left="372" top="2592" width="13.5" height="17.25" align-x="378" align-y="2603.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="87"/> </region> </text> </region> <region region-id="346" left="36" top="2625" width="196.5" height="51" align-x="209.25" align-y="2652" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:sequence> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">∞</ml:id> </ml:bounds> </ml:apply> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> </math> <rendering item-idref="88"/> </region> <region region-id="348" left="270" top="2640.75" width="58.5" height="15.75" align-x="313.5" align-y="2652" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">T'</ml:id> <ml:sequence> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="89"/> </region> <region region-id="350" left="474" top="2640.75" width="21.75" height="15.75" align-x="483.75" align-y="2652" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>12</ml:real> </ml:parens> </math> <rendering item-idref="90"/> </region> <region region-id="713" left="24" top="2688.75" width="476.25" height="83.25" align-x="24" align-y="2700" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Константу V0, заданную на интервале 0<x<L, доопределим нечётным образом на отрезке </f> <f family="Arial Cyr" charset="204" size="12">(-L,0) и р</f> <f family="Arial Cyr" charset="204" size="12">азложим в ряд Фурье<sp count="3"/>по собственным функциям </f> <region region-id="352" left="390.75" top="2703" width="14.25" height="17.25" align-x="396.75" align-y="2714.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="91"/> </region> <f family="Arial Cyr" charset="204" size="12">:</f> <region region-id="370" left="24" top="2721" width="185.25" height="51" align-x="45.75" align-y="2748" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">V0</ml:id> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">V1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">∞</ml:id> </ml:bounds> </ml:apply> </ml:apply> </math> <rendering item-idref="92"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> .<sp count="6"/> </inlineAttr> </f> </text> </region> <region region-id="1060" left="30" top="2832.75" width="476.25" height="108" align-x="30" align-y="2844" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">В общем случае коэффициент ряда Фурье V1</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12"> функции V0 определяется так:</f> <region region-id="1061" left="30" top="2850" width="129" height="90.75" align-x="57" align-y="2898" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">V1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">V0</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:bounds> </ml:apply> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:bounds> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="93"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, здесь </inlineAttr> </f> <region region-id="1062" left="200.25" top="2886" width="23.25" height="16.5" align-x="207.75" align-y="2898" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </math> <rendering item-idref="94"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> - вес собственной функции </inlineAttr> </f> <region region-id="1064" left="376.5" top="2886.75" width="14.25" height="17.25" align-x="382.5" align-y="2898" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="95"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, равный единице.</inlineAttr> </f> </text> </region> <region region-id="1069" left="30" top="2970.75" width="219" height="13.5" align-x="30" align-y="2982" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Используя формулы (4a) и (4b), найдём:</f> </text> </region> <region region-id="1077" left="288" top="2970" width="42" height="16.5" align-x="311.25" align-y="2982" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">nor</ml:id> <ml:symResult> <ml:id xml:space="preserve">π</ml:id> </ml:symResult> </ml:symEval> </math> <rendering item-idref="96"/> </region> <region region-id="1078" left="348" top="2970" width="57.75" height="16.5" align-x="377.25" align-y="2982" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">nor1</ml:id> <ml:symResult> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="97"/> </region> <region region-id="1085" left="30" top="3000.75" width="403.5" height="55.5" align-x="72.75" align-y="3030" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V1a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> </ml:function> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">nor</ml:id> </ml:apply> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">V0</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:bounds> </ml:apply> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">substitute</ml:id> <ml:apply> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </ml:sequence> </ml:command> <ml:symResult> <ml:apply> <ml:div/> <ml:real>4</ml:real> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </ml:define> </math> <rendering item-idref="98"/> </region> <region region-id="1091" left="36" top="3099" width="428.25" height="64.5" align-x="79.5" align-y="3132" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V1b</ml:id> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> </ml:function> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">nor1</ml:id> </ml:apply> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">V0</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:bounds> </ml:apply> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">substitute</ml:id> <ml:apply> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </ml:sequence> </ml:command> <ml:command> <ml:sequence> <ml:id xml:space="preserve">substitute</ml:id> <ml:apply> <ml:equal/> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:sequence> </ml:command> <ml:command> <ml:id xml:space="preserve">simplify</ml:id> </ml:command> <ml:symResult> <ml:apply> <ml:div/> <ml:real>4</ml:real> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </ml:define> </math> <rendering item-idref="99"/> </region> <region region-id="1092" left="36" top="3186.75" width="466.5" height="62.25" align-x="36" align-y="3198" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Из полученных значений коэффициентов ряда Фурье следует то, что константу V0</f> <f family="Arial Cyr" charset="204" size="12">не обязательно было доопределять как нечетную функцию на отрезке [-L,0]. </f> <f family="Arial Cyr" charset="204" size="12">Далее за коэффициент ряда Фурье примем: </f> <region region-id="1093" left="280.5" top="3214.5" width="93.75" height="34.5" align-x="307.5" align-y="3234" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">V1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="100"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> </text> </region> <region region-id="516" left="36" top="3270.75" width="394.5" height="13.5" align-x="36" align-y="3282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Построим график функции VK(x), представляющий данную константу V0:</f> </text> </region> <region region-id="514" left="54" top="3297.75" width="255.75" height="50.25" align-x="94.5" align-y="3324" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">VK</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">V0</ml:id> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>4</ml:real> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:real>100</ml:real> </ml:bounds> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="101"/> </region> <region region-id="515" left="354" top="3318.75" width="92.25" height="15.75" align-x="403.5" align-y="3330" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">VK</ml:id> <ml:real>1.9</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.99487283758323108</ml:real> </result> </ml:eval> </math> <rendering item-idref="102"/> </region> <region region-id="548" left="474" top="3318.75" width="21.75" height="15.75" align-x="483.75" align-y="3330" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>13</ml:real> </ml:parens> </math> <rendering item-idref="103"/> </region> <region region-id="519" left="54" top="3354" width="176.25" height="115.5" align-x="54" align-y="3354" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="104"/> <rendering item-idref="105"/> </region> <region region-id="1107" left="288" top="3396.75" width="190.5" height="30" align-x="288" align-y="3408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Здесь 2L - полупериод, так как</f> <region region-id="848" left="288" top="3411" width="33" height="15.75" align-x="305.25" align-y="3422.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">VK</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </math> <rendering item-idref="106"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> имеет период 4L</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">.</f> </text> </region> <region region-id="699" left="36" top="3510.75" width="227.25" height="13.5" align-x="36" align-y="3522" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Таким образом, получены два уравнения:</f> </text> </region> <region region-id="707" left="42" top="3546.75" width="69.75" height="17.25" align-x="83.25" align-y="3558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:sequence> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">V1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="107"/> </region> <region region-id="708" left="162" top="3546.75" width="58.5" height="15.75" align-x="205.5" align-y="3558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">T'</ml:id> <ml:sequence> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="108"/> </region> <region region-id="1115" left="420" top="3546.75" width="27" height="15.75" align-x="432.75" align-y="3558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:mult style="auto-select"/> <ml:real>12</ml:real> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:parens> </math> <rendering item-idref="109"/> </region> <region region-id="1108" left="36" top="3576.75" width="476.25" height="43.5" align-x="36" align-y="3588" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">из которых следует искать коэффициенты A</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12"> и B</f> <f family="Arial Cyr" charset="204" size="12"> n , </f> <f family="Arial Cyr" charset="204" size="12"> Определение<sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12">A</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12"> и B</f> <f family="Arial Cyr" charset="204" size="12">n </f> <f family="Arial Cyr" charset="204" size="12">будет </f> <f family="Arial Cyr" charset="204" size="12">дано ниже</f> <f family="Arial Cyr" charset="204" size="12">. Само же решение (resh), исходя из принципа суперпозиции теперь </f> <f family="Arial Cyr" charset="204" size="12">будет иметь вид:</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="716" left="432" top="3642.75" width="32.25" height="15.75" align-x="447" align-y="3654" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Resh</ml:id> </ml:parens> </math> <rendering item-idref="110"/> </region> <region region-id="715" left="150" top="3633" width="211.5" height="51" align-x="189.75" align-y="3660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">V</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">∞</ml:id> </ml:bounds> </ml:apply> </ml:apply> </math> <rendering item-idref="111"/> </region> <region region-id="719" left="30" top="3696.75" width="455.25" height="43.5" align-x="30" align-y="3708" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Функция V(х,t) является нечетной периодической с периодом 4L (2L - полупериод) и представлена рядом Фурье в виде разложения по системе ортогональных функций {X</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">}</f> <f family="Arial Cyr" charset="204" size="12"> .</f> </text> </region> <region region-id="465" left="150" top="3756.75" width="159" height="14.25" align-x="150" align-y="3768" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Алгоритмизация решения. </f> </text> </region> <region region-id="964" left="42" top="3780.75" width="411.75" height="13.5" align-x="42" align-y="3792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Все задаваемые ниже параметры можно менять в интерактивном режиме.</f> </text> </region> <region region-id="961" left="42" top="3804.75" width="230.25" height="13.5" align-x="42" align-y="3816" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Зададим диапазон изменения индекса "n":</f> </text> </region> <region region-id="962" left="288" top="3804.75" width="54.75" height="15.75" align-x="314.25" align-y="3816" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">NN</ml:id> <ml:real>150</ml:real> </ml:define> </math> <rendering item-idref="112"/> </region> <region region-id="963" left="360" top="3804.75" width="57.75" height="15.75" align-x="373.5" align-y="3816" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">n</ml:id> <ml:range> <ml:real>1</ml:real> <ml:id xml:space="preserve">NN</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="113"/> </region> <region region-id="850" left="42" top="3827.25" width="450.75" height="17.25" align-x="42" align-y="3840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Погрешность округления<sp count="2"/>N до целого числа: </f> <region region-id="1002" left="288" top="3828" width="52.5" height="16.5" align-x="303" align-y="3840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIFunction" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ε</ml:id> <ml:real>0.001</ml:real> </ml:define> </math> <rendering item-idref="114"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Её можно задать как ноль.</inlineAttr> </f> </text> </region> <region region-id="733" left="42" top="3868.5" width="105" height="39.75" align-x="63" align-y="3894" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="115"/> </region> <region region-id="732" left="174" top="3867" width="200.25" height="47.25" align-x="198" align-y="3894" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="116"/> </region> <region region-id="546" left="42" top="3933" width="198.75" height="47.25" align-x="64.5" align-y="3960" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="117"/> </region> <region region-id="362" left="36" top="3990" width="441.75" height="31.5" align-x="36" align-y="4002" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Следовательно (см. (12а)), </f> <region region-id="363" left="186.75" top="3990.75" width="69.75" height="17.25" align-x="228" align-y="4002" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:sequence> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">V1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="118"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> и для всех случаев (всех n) </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false" line-through="false">1), 2), 3)</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> имеем:</inlineAttr> </f> </text> </region> <region region-id="476" left="108" top="4036.5" width="90" height="34.5" align-x="129.75" align-y="4056" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="119"/> </region> <region region-id="378" left="468" top="4050.75" width="21.75" height="15.75" align-x="477.75" align-y="4062" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>14</ml:real> </ml:parens> </math> <rendering item-idref="120"/> </region> <region region-id="855" left="42" top="4086.75" width="321.75" height="13.5" align-x="42" align-y="4098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Проверка и вывод на экран монитора численных значений:</f> </text> </region> <region region-id="856" left="384" top="4086.75" width="69" height="17.25" align-x="410.25" align-y="4098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:real>50</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.012861005502375381</ml:real> </result> </ml:eval> </math> <rendering item-idref="121"/> </region> <region region-id="858" left="42" top="4110.75" width="474.75" height="37.5" align-x="42" align-y="4122" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Второе условие в (12) даст </f> <f family="Arial Cyr" charset="204" size="12">для всех случаев (всех n) </f> <f family="Arial Cyr" charset="204" size="12"> 1), 2), 3) </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal">, считая для случая 3) </inlineAttr> </f> <region region-id="379" left="42" top="4125.75" width="39.75" height="18" align-x="66.75" align-y="4137.75" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="122"/> </region> <f family="Arial Cyr" charset="204" size="12"> : </f> <region region-id="381" left="90" top="4125.75" width="90.75" height="18" align-x="165.75" align-y="4137.75" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">ν</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="123"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false" line-through="false">. </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Что в свою очередь позволит вычислить B</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="1114" left="42" top="4158" width="448.5" height="36.75" align-x="42" align-y="4170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> 1а) Для </f> <region region-id="391" left="87.75" top="4158.75" width="30.75" height="15.75" align-x="100.5" align-y="4170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessThan/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </math> <rendering item-idref="124"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (корни p1</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, p2</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>действительные разные). </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">Введем константы N1, N2 и К для вычисления В</f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, записываемых в вектор В</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> </text> </region> <region region-id="449" left="48" top="4244.25" width="133.5" height="36.75" align-x="71.25" align-y="4266" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N1</ml:id> <ml:apply> <ml:id xml:space="preserve">floor</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="125"/> </region> <region region-id="862" left="210" top="4254.75" width="67.5" height="15.75" align-x="233.25" align-y="4266" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N2</ml:id> <ml:apply> <ml:id xml:space="preserve">ceil</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="126"/> </region> <region region-id="863" left="42" top="4290.75" width="321.75" height="13.5" align-x="42" align-y="4302" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Проверка и вывод на экран монитора численных значений:</f> </text> </region> <region region-id="871" left="42" top="4320.75" width="44.25" height="15.75" align-x="64.5" align-y="4332" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N1</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="127"/> </region> <region region-id="872" left="126" top="4320.75" width="44.25" height="15.75" align-x="148.5" align-y="4332" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N2</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>2</ml:real> </result> </ml:eval> </math> <rendering item-idref="128"/> </region> <region region-id="873" left="210" top="4320.75" width="47.25" height="15.75" align-x="226.5" align-y="4332" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.5</ml:real> </result> </ml:eval> </math> <rendering item-idref="129"/> </region> <region region-id="861" left="36" top="4345.5" width="456.75" height="75" align-x="36" align-y="4368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Таким образом, N1 - это наибольшее целое число, не превосходящее<sp count="2"/> </f> <region region-id="271" left="421.5" top="4346.25" width="65.25" height="36.75" align-x="469.5" align-y="4368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="130"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, а N2 - наименьшее целое число, большее или равное<sp count="2"/> </inlineAttr> </f> <region region-id="874" left="332.25" top="4383.75" width="65.25" height="36.75" align-x="380.25" align-y="4405.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="131"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> </text> </region> <region region-id="953" left="42" top="4434.75" width="319.5" height="13.5" align-x="42" align-y="4446" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Сформируем логический программный блок вычисления К</f> </text> </region> <region region-id="875" left="24" top="4476" width="237" height="80.25" align-x="41.25" align-y="4488" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">K</ml:id> <ml:program> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:lessThan/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N2</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:lessOrEqual/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:id xml:space="preserve">ε</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">N1</ml:id> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:lessThan/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N2</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:lessOrEqual/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N2</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:id xml:space="preserve">ε</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">N2</ml:id> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:ifThen> <ml:otherwise> <ml:real>0</ml:real> </ml:otherwise> </ml:program> </ml:define> </math> <rendering item-idref="132"/> </region> <region region-id="888" left="36" top="4578.75" width="321.75" height="13.5" align-x="36" align-y="4590" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Проверка и вывод на экран монитора численных значений:</f> </text> </region> <region region-id="893" left="378" top="4578.75" width="38.25" height="15.75" align-x="394.5" align-y="4590" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">K</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="133"/> </region> <region region-id="971" left="36" top="4602" width="419.25" height="33" align-x="36" align-y="4614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Если </f> <region region-id="904" left="65.25" top="4602.75" width="31.5" height="15.75" align-x="81.75" align-y="4614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:id xml:space="preserve">K</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="134"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, то номер n=K соответствует действительным равным корням,</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">в противном случае </f> <f family="Arial Cyr" charset="204" size="12">корни p1</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">, p2</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>действительные разные.</f> </text> </region> <region region-id="720" left="36" top="4649.25" width="469.5" height="44.25" align-x="36" align-y="4662" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Здесь и далее логическое равенство<sp count="2"/> </f> <region region-id="721" left="245.25" top="4650.75" width="40.5" height="15.75" align-x="267.75" align-y="4662" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </math> <rendering item-idref="135"/> </region> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>заменено неравенством </f> <region region-id="722" left="429.75" top="4650" width="60.75" height="16.5" align-x="474" align-y="4662" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessOrEqual/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:id xml:space="preserve">ε</ml:id> </ml:apply> </math> <rendering item-idref="136"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">так как практически невозможно задать N<sp count="2"/>как целое число. Н</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">еравенство</f> <f family="Arial Cyr" charset="204" size="12"> же </f> <f family="Arial Cyr" charset="204" size="12">позволяет </f> <f family="Arial Cyr" charset="204" size="12">искусственно создать в алгоритме эту ситуацию целого числа N.</f> </text> </region> <region region-id="954" left="36" top="4704.75" width="332.25" height="16.5" align-x="36" align-y="4716" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Теперь можно приступить к вычислению коэффициентов В</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">: </f> </text> </region> <region region-id="946" left="36" top="4734.75" width="139.5" height="15.75" align-x="62.25" align-y="4746" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">KK</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">N1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="137"/> </region> <region region-id="947" left="198" top="4734.75" width="47.25" height="15.75" align-x="223.5" align-y="4746" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">KK</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="138"/> </region> <region region-id="892" left="48" top="4770.75" width="57.75" height="15.75" align-x="61.5" align-y="4782" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">n</ml:id> <ml:range> <ml:real>1</ml:real> <ml:id xml:space="preserve">KK</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="139"/> </region> <region region-id="891" left="204" top="4767.75" width="283.5" height="57.75" align-x="225" align-y="4788" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:program> <ml:ifThen> <ml:apply> <ml:or/> <ml:parens> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">K</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:lessThan/> <ml:apply> <ml:lessOrEqual/> <ml:real>1</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">ν</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:ifThen> <ml:otherwise> <ml:real>0</ml:real> </ml:otherwise> </ml:program> </ml:define> </math> <rendering item-idref="140"/> </region> <region region-id="753" left="36" top="4848.75" width="321.75" height="13.5" align-x="36" align-y="4860" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Проверка и вывод на экран монитора численных значений:</f> </text> </region> <region region-id="980" left="54" top="4878.75" width="42" height="17.25" align-x="74.25" align-y="4890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="141"/> </region> <region region-id="979" left="132" top="4878.75" width="57" height="17.25" align-x="152.25" align-y="4890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:real>1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.4702103877914459</ml:real> </result> </ml:eval> </math> <rendering item-idref="142"/> </region> <region region-id="978" left="222" top="4878.75" width="41.25" height="17.25" align-x="242.25" align-y="4890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="index out of bounds" optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:eval> </math> <rendering item-idref="143"/> </region> <region region-id="977" left="330" top="4878.75" width="41.25" height="17.25" align-x="350.25" align-y="4890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="index out of bounds" optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:eval> </math> <rendering item-idref="144"/> </region> <region region-id="487" left="36" top="4950" width="480" height="60.75" align-x="36" align-y="4962" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10"> Примечание. </f> <f family="Arial Cyr" charset="204" size="10"> Если условия </f> <region region-id="488" left="162.75" top="4950.75" width="132.75" height="15.75" align-x="210" align-y="4962" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:or/> <ml:parens> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">K</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:lessThan/> <ml:apply> <ml:lessOrEqual/> <ml:real>1</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </ml:parens> </ml:apply> </math> <rendering item-idref="145"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> не выполнены, то B</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">можно не вычислять </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">или приравнять любой константе, в т. ч. нулю, т. к. формула решения будет другой. Поэтому опцию n=1..K-1 верную при</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="938" left="132" top="4983" width="32.25" height="15.75" align-x="148.5" align-y="4994.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">K</ml:id> <ml:real>2</ml:real> </ml:apply> </math> <rendering item-idref="146"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> и дающую сбой при K=0 следует заменить на n=1..KK, где KK=if(</inlineAttr> </f> <region region-id="965" left="467.25" top="4983" width="32.25" height="15.75" align-x="483.75" align-y="4994.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="147"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="10">, K-1, N1</f> </inlineAttr> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> ). </inlineAttr> </f> </text> </region> <region region-id="387" left="48" top="5028" width="249.75" height="20.25" align-x="48" align-y="5040" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> 2а)<sp count="2"/>Для </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="392" left="96.75" top="5028.75" width="30.75" height="15.75" align-x="109.5" align-y="5040" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterThan/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </math> <rendering item-idref="148"/> </region> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">(корни </f> <f family="Arial Cyr" charset="204" size="12">p1</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">, p2</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12"> комплексные)</f> </text> </region> <region region-id="900" left="48" top="5064.75" width="129.75" height="15.75" align-x="61.5" align-y="5076" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">n</ml:id> <ml:range> <ml:apply> <ml:id xml:space="preserve">max</ml:id> <ml:sequence> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">N2</ml:id> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">NN</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="149"/> </region> <region region-id="899" left="204" top="5055.75" width="110.25" height="36.75" align-x="225" align-y="5076" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">ν</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="150"/> </region> <region region-id="735" left="42" top="5106.75" width="321.75" height="13.5" align-x="42" align-y="5118" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Проверка и вывод на экран монитора численных значений:</f> </text> </region> <region region-id="901" left="378" top="5106.75" width="57.75" height="15.75" align-x="414" align-y="5118" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="151"/> </region> <region region-id="902" left="456" top="5106.75" width="44.25" height="15.75" align-x="478.5" align-y="5118" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N2</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>2</ml:real> </result> </ml:eval> </math> <rendering item-idref="152"/> </region> <region region-id="746" left="36" top="5142.75" width="65.25" height="17.25" align-x="64.5" align-y="5154" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.37960668982249446</ml:real> </result> </ml:eval> </math> <rendering item-idref="153"/> </region> <region region-id="747" left="108" top="5142.75" width="82.5" height="17.25" align-x="147.75" align-y="5154" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">N2</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.11113745888685707</ml:real> </result> </ml:eval> </math> <rendering item-idref="154"/> </region> <region region-id="748" left="204" top="5142.75" width="82.5" height="17.25" align-x="243.75" align-y="5154" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">N2</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.054229527117499204</ml:real> </result> </ml:eval> </math> <rendering item-idref="155"/> </region> <region region-id="749" left="312" top="5142.75" width="30" height="13.5" align-x="312" align-y="5154" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">и т. д.</f> </text> </region> <region region-id="750" left="366" top="5137.5" width="105.75" height="22.5" align-x="391.5" align-y="5154" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:real>51</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.00024967929585565751</ml:real> </result> </ml:eval> </math> <rendering item-idref="156"/> </region> <region region-id="395" left="48" top="5178" width="432.75" height="20.25" align-x="48" align-y="5190" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> 3а)<sp count="2"/>Для </f> <region region-id="409" left="96.75" top="5178.75" width="30.75" height="15.75" align-x="109.5" align-y="5190" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </math> <rendering item-idref="157"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (если<sp count="2"/>N целое, корни p1</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, p2</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>действительные равные)</inlineAttr> </f> </text> </region> <region region-id="394" left="66" top="5211.75" width="165" height="56.25" align-x="88.5" align-y="5232" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">K</ml:id> </ml:apply> <ml:program> <ml:ifThen> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">K</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">ν</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">K</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:ifThen> <ml:otherwise> <ml:real>0</ml:real> </ml:otherwise> </ml:program> </ml:define> </math> <rendering item-idref="158"/> </region> <region region-id="758" left="36" top="5292.75" width="321.75" height="13.5" align-x="36" align-y="5304" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Проверка и вывод на экран монитора численных значений:</f> </text> </region> <region region-id="996" left="36" top="5322.75" width="38.25" height="15.75" align-x="52.5" align-y="5334" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">K</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="159"/> </region> <region region-id="995" left="90" top="5322.75" width="42" height="17.25" align-x="110.25" align-y="5334" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="160"/> </region> <region region-id="994" left="150" top="5322.75" width="43.5" height="17.25" align-x="171.75" align-y="5334" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">K</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="161"/> </region> <region region-id="993" left="216" top="5322.75" width="69.75" height="17.25" align-x="249" align-y="5334" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.4702103877914459</ml:real> </result> </ml:eval> </math> <rendering item-idref="162"/> </region> <region region-id="399" left="24" top="5363.25" width="474.75" height="123.75" align-x="24" align-y="5376" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">В общем же случае, когда </f> <region region-id="397" left="168" top="5364" width="74.25" height="16.5" align-x="210.75" align-y="5376" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">V</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="163"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">,<sp count="2"/> </inlineAttr> </f> <region region-id="398" left="252" top="5364" width="81.75" height="18" align-x="300" align-y="5376" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:apply> <ml:id xml:space="preserve">V'</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="164"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> , будем иметь ([20], Будак, стр.231)</inlineAttr> </f> <region region-id="400" left="24" top="5396.25" width="108.75" height="90.75" align-x="45" align-y="5444.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">L1</ml:id> </ml:bounds> </ml:apply> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">L1</ml:id> </ml:bounds> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="165"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>,<sp count="5"/> </inlineAttr> </f> <region region-id="402" left="157.5" top="5396.25" width="165.75" height="90.75" align-x="233.25" align-y="5444.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">ν</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">L1</ml:id> </ml:bounds> </ml:apply> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">L1</ml:id> </ml:bounds> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="166"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> . Где L1<sp count="2"/>заданный отрезок.</inlineAttr> </f> </text> </region> <region region-id="765" left="24" top="5514.75" width="419.25" height="72.75" align-x="24" align-y="5526" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Проверка </f> <f family="Arial Cyr" charset="204" size="12">. V1</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12"> определяется как коэффициент ряда Фурье: </f> <region region-id="774" left="24" top="5532" width="214.5" height="55.5" align-x="51" align-y="5561.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">V1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">V0</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:apply> <ml:mult style="default"/> <ml:real>-2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:bounds> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="167"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, где 2L норма, равная </inlineAttr> </f> <region region-id="775" left="366" top="5535" width="73.5" height="44.25" align-x="410.25" align-y="5561.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:apply> <ml:mult style="auto-select"/> <ml:real>-2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:bounds> </ml:apply> </math> <rendering item-idref="168"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="791" left="24" top="5664.75" width="94.5" height="13.5" align-x="24" align-y="5676" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Вычислим норму:</f> </text> </region> <region region-id="790" left="138" top="5641.5" width="180.75" height="60.75" align-x="290.25" align-y="5676" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:real>13</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">U</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:apply> <ml:mult style="default"/> <ml:real>-2</ml:real> <ml:id xml:space="preserve">U</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">U</ml:id> </ml:apply> </ml:bounds> </ml:apply> <ml:symResult> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">U</ml:id> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="169"/> </region> <region region-id="789" left="348" top="5664" width="53.25" height="16.5" align-x="372.75" align-y="5676" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:symResult> <ml:apply> <ml:mult style="default"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="170"/> </region> <region region-id="792" left="426" top="5664.75" width="27" height="13.5" align-x="426" align-y="5676" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">ч.т.д.</f> </text> </region> <region region-id="817" left="18" top="5742.75" width="152.25" height="13.5" align-x="18" align-y="5754" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Проверка ортогональности:</f> </text> </region> <region region-id="818" left="186" top="5724.75" width="241.5" height="55.5" align-x="411" align-y="5754" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:real>1</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:apply> <ml:mult style="auto-select"/> <ml:real>-2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:bounds> </ml:apply> <ml:symResult> <ml:real>0</ml:real> </ml:symResult> </ml:symEval> </math> <rendering item-idref="171"/> </region> <region region-id="794" left="246" top="5802.75" width="207" height="55.5" align-x="421.5" align-y="5832" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">V0</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:real>3</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:bounds> </ml:apply> </ml:apply> <ml:symResult> <ml:apply> <ml:div/> <ml:real>4</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>5</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="172"/> </region> <region region-id="795" left="24" top="5826.75" width="202.5" height="13.5" align-x="24" align-y="5838" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Вычислим коэффициент ряда Фурье:</f> </text> </region> <region region-id="1109" left="24" top="5868.75" width="482.25" height="16.5" align-x="24" align-y="5880" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">С другой стороны V1</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">=A</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">. Далее нетрудно убедиться в справедливости общих формул. </f> </text> </region> <region region-id="819" left="24" top="5910.75" width="201.75" height="13.5" align-x="24" align-y="5922" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Вывод на экран численных значений:</f> </text> </region> <region region-id="820" left="252" top="5902.5" width="53.25" height="34.5" align-x="273.75" align-y="5922" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:symResult> <ml:apply> <ml:div/> <ml:real>4</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>5</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="173"/> </region> <region region-id="821" left="36" top="5946.75" width="90" height="13.5" align-x="36" align-y="5958" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Конец проверки.</f> </text> </region> <region region-id="1100" left="30" top="5976.75" width="482.25" height="57" align-x="30" align-y="5988" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Решение задачи (1) - (2) имеет переменную структуру, зависимую от<sp count="2"/>констант </f> <f family="Arial Cyr" charset="204" size="12">K, N1, N2, разбивающих множество индексов n на подмножества. Каждому набору подмножеств индексов n соответствует своя формула решения с коэффициентами </f> <f family="Arial Cyr" charset="204" size="12">B</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">.</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="935" left="36" top="6042.75" width="476.25" height="13.5" align-x="36" align-y="6054" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Выпишем четыре формулы вычисления решения и пятую V6(x,t) </f> <f family="Arial Cyr" charset="204" size="12">:</f> </text> </region> <region region-id="917" left="42" top="6072" width="417" height="30" align-x="42" align-y="6084" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">1. Решение для К=0 и<sp count="2"/> </f> <region region-id="918" left="164.25" top="6072.75" width="93.75" height="15.75" align-x="234" align-y="6084" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessThan/> <ml:apply> <ml:lessThan/> <ml:apply> <ml:lessOrEqual/> <ml:real>1</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="174"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> . Корни действительные разные и комплексные.</inlineAttr> </f> </text> </region> <region region-id="423" left="48" top="6117.75" width="399.75" height="99" align-x="94.5" align-y="6144" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V1</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:bounds> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">NN</ml:id> </ml:bounds> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="175"/> </region> <region region-id="919" left="42" top="6240" width="391.5" height="30" align-x="42" align-y="6252" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">2. Решение для<sp count="2"/> </f> <region region-id="923" left="132" top="6240.75" width="32.25" height="15.75" align-x="148.5" align-y="6252" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">K</ml:id> <ml:real>2</ml:real> </ml:apply> </math> <rendering item-idref="176"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> .</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">Корни действительные разные, комплексные</f> <f family="Arial Cyr" charset="204" size="12">и </f> <f family="Arial Cyr" charset="204" size="12">действительные равные</f> <f family="Arial Cyr" charset="204" size="12">.</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="425" left="48" top="6351.75" width="393" height="131.25" align-x="94.5" align-y="6378" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V2</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:bounds> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">NN</ml:id> </ml:bounds> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">K</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">K</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">K</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="177"/> </region> <region region-id="926" left="60" top="6492.75" width="423" height="13.5" align-x="60" align-y="6504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">3. Решение для К=1. </f> <f family="Arial Cyr" charset="204" size="12">Корни<sp count="2"/>комплексные и </f> <f family="Arial Cyr" charset="204" size="12">действительные равные</f> <f family="Arial Cyr" charset="204" size="12">.</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="426" left="54" top="6525.75" width="379.5" height="82.5" align-x="100.5" align-y="6552" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V3</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>2</ml:real> <ml:id xml:space="preserve">NN</ml:id> </ml:bounds> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="178"/> </region> <region region-id="929" left="60" top="6624.75" width="240.75" height="13.5" align-x="60" align-y="6636" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">4. Решение для N1=0 . </f> <f family="Arial Cyr" charset="204" size="12">Корни<sp count="2"/>комплексные.</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="429" left="48" top="6657.75" width="366" height="50.25" align-x="94.5" align-y="6684" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V4</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">NN</ml:id> </ml:bounds> </ml:apply> </ml:define> </math> <rendering item-idref="179"/> </region> <region region-id="554" left="48" top="6718.5" width="438" height="83.25" align-x="48" align-y="6744" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Поледнее выражение, получаемое при </f> <region region-id="930" left="263.25" top="6719.25" width="61.5" height="45" align-x="275.25" align-y="6744" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterThan/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="180"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">,</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>можно преобразовать к виду, если ввести</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="558" left="147" top="6765" width="71.25" height="36.75" align-x="192.75" align-y="6786" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">cot</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="181"/> </region> <f family="Arial Cyr" charset="204" size="12"> :</f> </text> </region> <region region-id="563" left="102" top="6828.75" width="87" height="15.75" align-x="116.25" align-y="6840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">NN</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="182"/> </region> <region region-id="564" left="222" top="6819.75" width="82.5" height="36.75" align-x="243" align-y="6840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">acot</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ν</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="183"/> </region> <region region-id="568" left="348" top="6819.75" width="63" height="34.5" align-x="390" align-y="6840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessOrEqual/> <ml:apply> <ml:lessThan/> <ml:real>0</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="184"/> </region> <region region-id="562" left="54" top="6873.75" width="406.5" height="50.25" align-x="100.5" align-y="6900" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V5</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">NN</ml:id> </ml:bounds> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="185"/> </region> <region region-id="1045" left="36" top="6953.25" width="357" height="29.25" align-x="36" align-y="6966" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">5. Решение для К-> </f> <region region-id="1047" left="143.25" top="6954" width="9.75" height="16.5" align-x="147" align-y="6966" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="186"/> </region> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>и<sp count="2"/> </f> <region region-id="1048" left="171.75" top="6954.75" width="15.75" height="15.75" align-x="178.5" align-y="6966" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">N1</ml:id> </math> <rendering item-idref="187"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">-></inlineAttr> </f> <region region-id="1049" left="198.75" top="6954" width="9.75" height="16.5" align-x="202.5" align-y="6966" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="188"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>. Корни действительные разные </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(В</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> этом файле эта формула не работает. См. "ВолнУр123_Алгоритм").</inlineAttr> </f> </text> </region> <region region-id="1046" left="42" top="7041.75" width="379.5" height="50.25" align-x="88.5" align-y="7068" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V6</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:bounds> </ml:apply> </ml:define> </math> <rendering item-idref="189"/> </region> <region region-id="968" left="42" top="7104.75" width="396.75" height="30" align-x="42" align-y="7116" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Вывод на экран монитора численных значений параметров, по которым </f> <f family="Arial Cyr" charset="204" size="12">выбирается одна из четырёх формул: </f> <region region-id="969" left="252.75" top="7119" width="38.25" height="15.75" align-x="269.25" align-y="7130.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">K</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="190"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">,<sp count="2"/> </inlineAttr> </f> <region region-id="970" left="300.75" top="7119" width="44.25" height="15.75" align-x="323.25" align-y="7130.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N1</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="191"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, </inlineAttr> </f> <region region-id="1007" left="351.75" top="7119" width="44.25" height="15.75" align-x="374.25" align-y="7130.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N2</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>2</ml:real> </result> </ml:eval> </math> <rendering item-idref="192"/> </region> </text> </region> <region region-id="571" left="54" top="7146.75" width="282" height="13.5" align-x="54" align-y="7158" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Логический блок выбора одной из четырех формул:</f> </text> </region> <region region-id="413" left="42" top="7182.75" width="202.5" height="100.5" align-x="82.5" align-y="7194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">K</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">V1</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">K</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">V2</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">V3</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">V5</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">∞</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">V6</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:ifThen> </ml:program> </ml:define> </math> <rendering item-idref="193"/> </region> <region region-id="1004" left="288" top="7182.75" width="162" height="100.5" align-x="303" align-y="7194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">fr</ml:id> <ml:program> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">K</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:str xml:space="preserve">V1</ml:str> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">K</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:str xml:space="preserve">V2</ml:str> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:str xml:space="preserve">V3</ml:str> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:str xml:space="preserve">V5</ml:str> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">∞</ml:id> </ml:apply> <ml:str xml:space="preserve">V6</ml:str> </ml:ifThen> </ml:program> </ml:define> </math> <rendering item-idref="194"/> </region> <region region-id="550" left="480" top="7188.75" width="21.75" height="15.75" align-x="489.75" align-y="7200" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>15</ml:real> </ml:parens> </math> <rendering item-idref="195"/> </region> <region region-id="1005" left="54" top="7314" width="407.25" height="16.5" align-x="54" align-y="7326" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Выбрана формула решения: </f> <region region-id="1006" left="213" top="7314.75" width="53.25" height="15.75" align-x="227.25" align-y="7326" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">fr</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">V1</ml:str> </result> </ml:eval> </math> <rendering item-idref="196"/> </region> </text> </region> <region region-id="1008" left="48" top="7334.25" width="444.75" height="24" align-x="48" align-y="7344" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">Можно дать следующее описание подмножеств множества индексов n, эквивалентное приведён-</f> <f family="Arial Cyr" charset="204" size="10">ному в (15), если положить </f> <f family="Symbol" charset="2" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">e</inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">=0 </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Описание приводится в той же последовательности, что и в (15).</inlineAttr> </f> </text> </region> <region region-id="1009" left="48" top="7368" width="435.75" height="37.5" align-x="48" align-y="7380" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">1. Выбор параметров: </f> <region region-id="1010" left="150" top="7368.75" width="46.5" height="15.75" align-x="172.5" align-y="7380" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="197"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> and </inlineAttr> </f> <region region-id="1011" left="219" top="7368.75" width="38.25" height="15.75" align-x="241.5" align-y="7380" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="198"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> приводит к разбиению на подмножества:</inlineAttr> </f> <region region-id="1012" left="48" top="7386" width="48.75" height="15.75" align-x="60.75" align-y="7397.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1..</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="199"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(корни </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10">p1</f> <f family="Arial Cyr" charset="204" size="10"> n </f> <f family="Arial Cyr" charset="204" size="10">, p2</f> <f family="Arial Cyr" charset="204" size="10"> n </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> действительные разные), </inlineAttr> </f> <region region-id="1013" left="288" top="7386" width="36.75" height="15.75" align-x="300.75" align-y="7397.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="200"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">..</inlineAttr> </f> <region region-id="1014" left="331.5" top="7385.25" width="9.75" height="16.5" align-x="335.25" align-y="7397.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="201"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> комплексные).</inlineAttr> </f> </text> </region> <region region-id="1015" left="48" top="7416" width="447.75" height="57.75" align-x="48" align-y="7428" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">2. Выбор параметров: </f> <region region-id="1017" left="150" top="7416.75" width="46.5" height="15.75" align-x="172.5" align-y="7428" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="202"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> and </inlineAttr> </f> <region region-id="1018" left="219" top="7416.75" width="38.25" height="15.75" align-x="241.5" align-y="7428" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>2</ml:real> </ml:apply> </math> <rendering item-idref="203"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> приводит к разбиению на подмножества:</inlineAttr> </f> <region region-id="1019" left="48" top="7433.25" width="67.5" height="15.75" align-x="60.75" align-y="7444.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1..</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="204"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204">n</f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="10"> действительные разные), </f> </inlineAttr> <region region-id="1016" left="306.75" top="7433.25" width="36.75" height="15.75" align-x="319.5" align-y="7444.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> </math> <rendering item-idref="205"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="10"> <sp/> </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(</inlineAttr> </f> <f family="Arial Cyr" charset="204">корни </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204"> действительные равные),</f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="10"> <sp/> </f> </inlineAttr> <region region-id="1020" left="90" top="7454.25" width="56.25" height="15.75" align-x="102.75" align-y="7465.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="206"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">..</inlineAttr> </f> <region region-id="1021" left="153" top="7453.5" width="9.75" height="16.5" align-x="156.75" align-y="7465.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="207"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204">n</f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="10"> комплексные).</f> </inlineAttr> </text> </region> <region region-id="1023" left="48" top="7488" width="406.5" height="37.5" align-x="48" align-y="7500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">3. Выбор параметров: </f> <region region-id="1026" left="150" top="7488.75" width="46.5" height="15.75" align-x="172.5" align-y="7500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="208"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> and </inlineAttr> </f> <region region-id="1027" left="219" top="7488.75" width="37.5" height="15.75" align-x="241.5" align-y="7500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="209"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> приводит к разбиению на подмножества:</inlineAttr> </f> <region region-id="1028" left="48" top="7506" width="27.75" height="15.75" align-x="60.75" align-y="7517.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="210"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> действительные равные), </inlineAttr> </f> <region region-id="1029" left="267.75" top="7506" width="27.75" height="15.75" align-x="280.5" align-y="7517.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:real>2</ml:real> </ml:apply> </math> <rendering item-idref="211"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">..</inlineAttr> </f> <region region-id="1030" left="302.25" top="7505.25" width="9.75" height="16.5" align-x="306" align-y="7517.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="212"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> комплексные).</inlineAttr> </f> </text> </region> <region region-id="1025" left="48" top="7535.25" width="451.5" height="33" align-x="48" align-y="7548" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">4. Выбор параметров: </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="1032" left="153" top="7536.75" width="37.5" height="15.75" align-x="175.5" align-y="7548" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="213"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> приводит к разбиению на подмножества:</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="1034" left="382.5" top="7536.75" width="27.75" height="15.75" align-x="395.25" align-y="7548" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="214"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">..</inlineAttr> </f> <region region-id="1035" left="417" top="7536" width="9.75" height="16.5" align-x="420.75" align-y="7548" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="215"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204">n</f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> комплексные).</inlineAttr> </f> </text> </region> <region region-id="1040" left="48" top="7577.25" width="331.5" height="37.5" align-x="48" align-y="7590" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204">5. Выбор параметров:</f> <f family="Arial Cyr" charset="204"> <sp/> </f> <region region-id="1041" left="150" top="7578.75" width="15.75" height="15.75" align-x="156.75" align-y="7590" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">N1</ml:id> </math> <rendering item-idref="216"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">-></inlineAttr> </f> <region region-id="1042" left="175.5" top="7578" width="9.75" height="16.5" align-x="179.25" align-y="7590" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="217"/> </region> <f family="Arial Cyr" charset="204"> <sp count="2"/>приводит к разбиению на подмножества:</f> <region region-id="1037" left="48" top="7595.25" width="48.75" height="15.75" align-x="60.75" align-y="7606.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1..</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="218"/> </region> <f family="Arial Cyr" charset="204"> <sp/> </f> <f family="Arial Cyr" charset="204">(корни </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204"> действительные разные)</f> </text> </region> <region region-id="1110" left="42" top="7644.75" width="198" height="13.5" align-x="42" align-y="7656" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Возможна анимация по параметру t:</f> </text> </region> <region region-id="1111" left="276" top="7636.5" width="80.25" height="33.75" align-x="287.25" align-y="7656" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">t</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>10</ml:real> </ml:apply> <ml:id xml:space="preserve">FRAME</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="219"/> </region> <region region-id="1112" left="390" top="7644.75" width="92.25" height="15.75" align-x="439.5" align-y="7656" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">V</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>10</ml:real> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.17258531028748556</ml:real> </result> </ml:eval> </math> <rendering item-idref="220"/> </region> <region region-id="236" left="54" top="7740" width="381.75" height="175.5" align-x="54" align-y="7740" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="221"/> <rendering item-idref="222"/> </region> <region region-id="68" left="48" top="7944" width="429.75" height="14.25" align-x="48" 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size="12"> <inlineAttr underline="false">2) Уменьшение R сильно увеличивает колебательность процесса и наоборот - увеличение R уменьшает колебательность.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr underline="false">3) Увеличение самоиндукции J замедляет процесс и уменьшает колебательность.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr underline="false">4) Ситуация n=N - целое число (<sp count="2"/> </inlineAttr> </f> <region region-id="937" left="244.5" top="8548.5" width="32.25" height="15.75" align-x="261" align-y="8559.75" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">N</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="234"/> </region> <f family="Arial Cyr" charset="204" size="12"> 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