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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">U2</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="1054" left="30" top="156.75" width="491.25" height="40.5" align-x="30" align-y="168" 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 Вы хотите сравнить полученное Вами решение с ответом, откройте в электрон-</f> <f family="Arial Cyr" charset="204" size="12">ной версии пособия ниже представленную закрытую область (в печатной версии</f> <f family="Arial Cyr" charset="204" size="12"> пособия она открыта).</f> </text> </region> <region region-id="1053" left="0" top="213" width="6008.25" align-x="8.25" align-y="222" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="" height="1004.25"> <area is-collapsed="false" name="" show-name="false" show-border="true" show-icon="true" show-timestamp="true" allow-expand="false" is-locked="false" timestamp="" top-lock-id="1053" bottom-lock-id="1081" bottom-tag=""> <region region-id="1055" left="30" top="222" width="54.75" height="14.25" align-x="30" align-y="234" 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 </f> </text> </region> <region region-id="1095" left="108" top="222.75" width="66" height="13.5" align-x="108" align-y="234" 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">Вычисляем:</f> </text> </region> <region region-id="1102" left="30" top="252.75" width="179.25" height="13.5" align-x="30" align-y="264" 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-я производная от у(х) по х:</f> </text> </region> <region region-id="1108" left="234" top="243" width="190.5" height="36.75" align-x="300" align-y="264" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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</math> <rendering item-idref="14"/> </region> <region region-id="1104" left="36" top="282.75" width="222.75" height="13.5" align-x="36" align-y="294" 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-я производная </f> <f family="Arial Cyr" charset="204" size="12">от у(х) по х</f> <f family="Arial Cyr" charset="204" size="12">:</f> </text> </region> <region region-id="1060" left="30" top="306.75" width="398.25" height="40.5" align-x="96" align-y="330" 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">U4</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <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">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:sequence> </ml:apply> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">y1</ml:id> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">y1</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:sequence> </ml:apply> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="1122" left="24" top="360.75" width="132.75" height="13.5" align-x="24" align-y="372" 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 дискрет по "x":</f> </text> </region> <region region-id="1121" left="174" top="360.75" width="39.75" height="15.75" align-x="194.25" align-y="372" 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">bb</ml:id> 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branch-id="00000000-0000-0000-0000-000000000000" revision-num="18" is-modified="true" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\МетПрипасовывания.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="dd62d7d7-9936-4965-89ae-cf836ae1798f" version-id="83f4ef56-4acf-4249-a0d2-c23a8eed5382" branch-id="00000000-0000-0000-0000-000000000000" revision-num="18" is-modified="true" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\МетПрипасовывания.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">3e12f53fd8713748a113d0c3aa0bffc1</contentHash> <ml:define> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">k</ml:id> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="22"> <element-image-map> <box left="1.5" top="0.75" width="65.25" height="15.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="950" left="54" top="438" width="443.25" height="14.25" align-x="54" 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"> Алгоритм решения </f> <f family="Arial Cyr" charset="204" size="12"> дифференциального уравнения : </f> </text> </region> 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<ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">W4</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:factorial/> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">W1</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">W2</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">W3</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:factorial/> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">W4</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:factorial/> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:localDefine> </ml:program> </ml:for> <ml:id xml:space="preserve">y</ml:id> </ml:program> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="1039" left="48" top="726.75" width="391.5" height="13.5" align-x="48" align-y="738" 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">Дискретные значения первой производной от полученного решения "y" :</f> </text> </region> <region region-id="952" left="42" top="765" width="403.5" height="32.25" align-x="76.5" align-y="786" 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">y1</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve">U1</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:sequence> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">U2</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">U3</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:sequence> </ml:apply> <ml:apply> <ml:factorial/> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">U4</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:sequence> </ml:apply> <ml:apply> <ml:factorial/> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="958" left="60" top="834" width="195" height="137.25" align-x="60" align-y="834" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="25"/> <rendering item-idref="26"/> </region> <region region-id="1016" left="384" top="894.75" width="111.75" height="40.5" align-x="384" 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">Возможна анимация</f> <f family="Arial Cyr" charset="204" size="12">графика. </f> <f family="Arial Cyr" charset="204" size="12">Рис. 1</f> <f family="Arial Cyr" charset="204" size="12">Вернуться назад.</f> </text> <link href="./МетПрипасовывания.xmcd" title="назад" popup="false"/> </region> <region region-id="1015" left="36" top="1002" width="296.25" height="191.25" align-x="36" align-y="1002" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="27"/> <rendering item-idref="28"/> </region> <region region-id="1026" left="414" top="1032.75" width="84" height="17.25" align-x="433.5" align-y="1044" 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">y</ml:id> <ml:id xml:space="preserve">K</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>3.8847394420606361E+48</ml:real> </result> </ml:eval> </math> <rendering item-idref="29"/> </region> <region region-id="961" left="402" top="1098.75" width="111.75" height="40.5" align-x="402" align-y="1110" 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</f> <f family="Arial Cyr" charset="204" size="12">графика.</f> <f family="Arial Cyr" charset="204" size="12">Рис. 2</f> </text> </region> </area> <rendering item-idref="30"/> </region> <region region-id="1175" left="18" top="1230.75" width="483" height="54.75" align-x="18" align-y="1242" 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">К Упражнению 1.</f> <f family="Arial Cyr" charset="204" size="12">Проверка решения, полученного методом припасовывания, путем сравнения с решением, полученным с помощью опции </f> <f family="Arial Cyr" charset="204" size="12"> Bulstoer </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">ШПО Mathcad </f> <f family="Arial Cyr" charset="204" size="10">(подробнее см. </f> <f family="Arial Cyr" charset="204" size="10">файл "РК2 пример задания </f> <f family="Arial Cyr" charset="204" size="10"> Bulstoer </f> <f family="Arial Cyr" charset="204" size="10">"</f> <f family="Arial Cyr" charset="204" size="10">)</f> <f family="Arial Cyr" charset="204" size="12">. </f> </text> </region> <region region-id="1150" left="24" top="1314.75" width="495" height="39" align-x="24" align-y="1326" 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">Параметры дифференциального уравнения и их условные обозначения взяты из </f> <f family="Arial Cyr" charset="204" size="12">таблицы РК 2 (выписать только числовые данные со </f> <f family="Arial Cyr" charset="204" size="12">знаком присвоения и функции).</f> <f family="Arial Cyr" charset="204" size="10"> Примечание </f> <f family="Arial Cyr" charset="204" size="10">. 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width="50.25" height="16.5" align-x="462.75" align-y="1404" 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">yy1</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="36"/> </region> <region region-id="1224" left="30" top="1440.75" width="287.25" height="13.5" align-x="30" align-y="1452" 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="false"> <f family="Arial Cyr" charset="204" size="12">Возьмём из выше приведенной библиотеки функций:</f> </text> </region> <region region-id="1157" left="30" top="1470.75" width="90.75" height="15.75" align-x="63" align-y="1482" show-border="false" 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top="1470.75" width="45.75" height="15.75" align-x="168.75" align-y="1482" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="7dc02276-53f4-44a4-99eb-1534bd554f2c" version-id="1ab2ea14-db2b-4ca2-92ed-f7b69c2f227e" branch-id="00000000-0000-0000-0000-000000000000" revision-num="7" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\Упражн2 С Bulstoer.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="7dc02276-53f4-44a4-99eb-1534bd554f2c" version-id="1ab2ea14-db2b-4ca2-92ed-f7b69c2f227e" branch-id="00000000-0000-0000-0000-000000000000" revision-num="7" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои 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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">f1</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">y</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="1197" left="324" top="1470.75" width="105" height="15.75" align-x="384.75" align-y="1482" 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">f2</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="40"/> </region> <region region-id="1159" left="30" top="1500.75" width="465.75" height="33" align-x="30" align-y="1512" 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">Запишем оператор D(x,z), задающий<sp count="2"/>правые части системы дифференциальных уравнений (здесь z</f> <f family="Arial Cyr" charset="204" size="12"> 0 </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">= y,<sp count="2"/>z</f> <f family="Arial Cyr" charset="204" size="12"> 1 </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">= y</f> <f family="Arial Cyr" charset="204" size="12">'</f> <f family="Arial Cyr" charset="204" size="12">), эквивалентной уравнению y</f> <f family="Arial Cyr" charset="204" size="12"> '' </f> <f family="Arial Cyr" charset="204" size="12">+ a*y</f> <f family="Arial Cyr" charset="204" size="12"> ' </f> <f family="Arial Cyr" charset="204" size="12">+ b*y = f(x)</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="1160" left="42" top="1567.5" width="162" height="38.25" align-x="85.5" align-y="1590" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="7dc02276-53f4-44a4-99eb-1534bd554f2c" 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<ml:real>1.4841093605960209</ml:real> <ml:real>19.99999999999995</ml:real> <ml:real>0.023252771693764905</ml:real> <ml:real>4.3369591588091794</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="50"/> </resultFormat> </math> <rendering item-idref="51"/> </region> <region region-id="1170" left="66" top="1896.75" width="361.5" height="13.5" align-x="66" align-y="1908" 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="false"> <f family="Arial Cyr" charset="204" size="12">Проверка решения в режиме анимации (~ 50 кадров) для f1(x,y,y1)</f> </text> </region> <region region-id="1208" left="72" top="1932" width="282" height="218.25" align-x="72" align-y="1932" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="52"/> <rendering item-idref="53"/> </region> <region region-id="1172" left="72" top="2184" width="387.75" height="14.25" align-x="72" align-y="2196" 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 режиме анимации используется<sp count="2"/>параметр </f> <f family="Arial Cyr" charset="204" size="12"> h </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal">.</inlineAttr> </f> </text> </region> <region region-id="1215" left="66" top="2214.75" width="429.75" height="13.5" align-x="66" align-y="2226" 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">Приведём отдельно графики функции f1</f> </text> </region> <region region-id="1209" left="54" top="2268" 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top="132.75" width="88.5" height="15.75" align-x="246.75" align-y="144" 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">U2</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="1054" left="30" top="156.75" width="491.25" height="40.5" align-x="30" align-y="168" 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 Вы хотите сравнить полученное Вами решение с ответом, откройте в электрон-</f> <f family="Arial Cyr" charset="204" size="12">ной версии пособия ниже представленную закрытую область (в печатной версии</f> <f family="Arial Cyr" charset="204" size="12"> пособия она открыта).</f> </text> </region> <region region-id="1053" left="0" top="213" width="6008.25" align-x="8.25" align-y="222" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="" height="1004.25"> <area is-collapsed="false" name="" show-name="false" show-border="true" show-icon="true" show-timestamp="true" allow-expand="false" is-locked="false" timestamp="" top-lock-id="1053" bottom-lock-id="1081" bottom-tag=""> <region region-id="1055" left="30" top="222" width="54.75" height="14.25" align-x="30" align-y="234" 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 </f> </text> </region> <region region-id="1095" left="108" top="222.75" width="66" height="13.5" align-x="108" align-y="234" 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">Вычисляем:</f> </text> </region> <region region-id="1102" left="30" top="252.75" width="179.25" height="13.5" align-x="30" align-y="264" 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-я производная от у(х) по х:</f> </text> </region> <region region-id="1108" left="234" top="243" width="190.5" height="36.75" align-x="300" align-y="264" 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">U3</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> </ml:function> <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">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="1104" left="36" top="282.75" width="222.75" height="13.5" align-x="36" align-y="294" 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-я производная </f> <f family="Arial Cyr" charset="204" size="12">от у(х) по х</f> <f family="Arial Cyr" charset="204" size="12">:</f> </text> </region> <region region-id="1060" left="30" top="306.75" width="398.25" height="40.5" align-x="96" align-y="330" 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 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xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">y1</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:sequence> </ml:apply> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="1122" left="24" top="360.75" width="132.75" height="13.5" align-x="24" align-y="372" 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 дискрет по "x":</f> </text> </region> <region region-id="1121" left="174" top="360.75" width="39.75" height="15.75" align-x="194.25" align-y="372" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" 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lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Алгоритм решения </f> <f family="Arial Cyr" charset="204" size="12"> дифференциального уравнения : </f> </text> </region> <region region-id="951" left="54" top="462.75" width="318" height="224.25" align-x="67.5" align-y="474" 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">y</ml:id> <ml:program> <ml:for> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:real>0</ml:real> <ml:id xml:space="preserve">K</ml:id> </ml:range> <ml:program> <ml:localDefine> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id 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<ml:id xml:space="preserve">W1</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">W2</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">W3</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:factorial/> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">W4</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:factorial/> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:localDefine> </ml:program> </ml:for> <ml:id xml:space="preserve">y</ml:id> </ml:program> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="1039" left="48" top="726.75" width="391.5" height="13.5" align-x="48" align-y="738" 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">Дискретные значения первой производной от полученного решения "y" :</f> </text> </region> <region region-id="952" left="42" top="765" width="403.5" height="32.25" align-x="76.5" align-y="786" 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">y1</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve">U1</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:sequence> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">U2</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">U3</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:sequence> </ml:apply> <ml:apply> <ml:factorial/> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">U4</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:sequence> </ml:apply> <ml:apply> <ml:factorial/> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="958" left="60" top="834" width="195" height="137.25" align-x="60" align-y="834" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="25"/> <rendering item-idref="26"/> </region> <region region-id="1016" left="384" top="894.75" width="111.75" height="40.5" align-x="384" 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">Возможна анимация</f> <f family="Arial Cyr" charset="204" size="12">графика. </f> <f family="Arial Cyr" charset="204" size="12">Рис. 1</f> <f family="Arial Cyr" charset="204" size="12">Вернуться назад.</f> </text> <link href="./МетПрипасовывания.xmcd" title="назад" popup="false"/> </region> <region region-id="1015" left="36" top="1002" width="296.25" height="191.25" align-x="36" align-y="1002" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="27"/> <rendering item-idref="28"/> </region> <region region-id="1026" left="414" top="1032.75" width="84" height="17.25" align-x="433.5" align-y="1044" 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">y</ml:id> <ml:id xml:space="preserve">K</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>3.8847394420606361E+48</ml:real> </result> </ml:eval> </math> <rendering item-idref="29"/> </region> <region region-id="961" left="402" top="1098.75" width="111.75" height="40.5" align-x="402" align-y="1110" 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</f> <f family="Arial Cyr" charset="204" size="12">графика.</f> <f family="Arial Cyr" charset="204" size="12">Рис. 2</f> </text> </region> </area> <rendering item-idref="30"/> </region> <region region-id="1175" left="18" top="1230.75" width="483" height="54.75" align-x="18" align-y="1242" 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">К Упражнению 1.</f> <f family="Arial Cyr" charset="204" size="12">Проверка решения, полученного методом припасовывания, путем сравнения с решением, полученным с помощью опции </f> <f family="Arial Cyr" charset="204" size="12"> Bulstoer </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">ШПО Mathcad </f> <f family="Arial Cyr" charset="204" size="10">(подробнее см. </f> <f family="Arial Cyr" charset="204" size="10">файл "РК2 пример задания </f> <f family="Arial Cyr" charset="204" size="10"> Bulstoer </f> <f family="Arial Cyr" charset="204" size="10">"</f> <f family="Arial Cyr" charset="204" size="10">)</f> <f family="Arial Cyr" charset="204" size="12">. </f> </text> </region> <region region-id="1150" left="24" top="1314.75" width="495" height="39" align-x="24" align-y="1326" 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">Параметры дифференциального уравнения и их условные обозначения взяты из </f> <f family="Arial Cyr" charset="204" size="12">таблицы РК 2 (выписать только числовые данные со </f> <f family="Arial Cyr" charset="204" size="12">знаком присвоения и функции).</f> <f family="Arial Cyr" charset="204" size="10"> Примечание </f> <f family="Arial Cyr" charset="204" size="10">. Все имена должны быть уникальными.</f> </text> </region> <region region-id="1151" left="102" top="1387.5" width="30.75" height="30.75" align-x="114.75" align-y="1404" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="7dc02276-53f4-44a4-99eb-1534bd554f2c" version-id="1ab2ea14-db2b-4ca2-92ed-f7b69c2f227e" branch-id="00000000-0000-0000-0000-000000000000" revision-num="7" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\Упражн2 С Bulstoer.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="7dc02276-53f4-44a4-99eb-1534bd554f2c" version-id="1ab2ea14-db2b-4ca2-92ed-f7b69c2f227e" branch-id="00000000-0000-0000-0000-000000000000" revision-num="7" 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xmlns="http://schemas.mathsoft.com/provenance10">c9c0dd4588febf94c36fa5bf9ae3a28b</contentHash> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:provenance> </math> <rendering item-idref="34"> <element-image-map> <box left="1.5" top="0.75" width="25.5" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1155" left="378" top="1392.75" width="39" height="16.5" align-x="397.5" align-y="1404" 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">y0</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="35"/> </region> <region region-id="1156" left="438" top="1392.75" width="50.25" height="16.5" align-x="462.75" align-y="1404" 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">yy1</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="36"/> </region> <region region-id="1224" left="30" top="1440.75" width="287.25" height="13.5" align-x="30" align-y="1452" 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="false"> <f family="Arial Cyr" charset="204" size="12">Возьмём из выше приведенной библиотеки функций:</f> </text> </region> <region region-id="1157" left="30" top="1470.75" width="90.75" height="15.75" align-x="63" align-y="1482" show-border="false" 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top="1470.75" width="45.75" height="15.75" align-x="168.75" align-y="1482" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="7dc02276-53f4-44a4-99eb-1534bd554f2c" version-id="1ab2ea14-db2b-4ca2-92ed-f7b69c2f227e" branch-id="00000000-0000-0000-0000-000000000000" revision-num="7" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\Упражн2 С Bulstoer.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="7dc02276-53f4-44a4-99eb-1534bd554f2c" version-id="1ab2ea14-db2b-4ca2-92ed-f7b69c2f227e" branch-id="00000000-0000-0000-0000-000000000000" revision-num="7" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои 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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">f1</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">y</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="1197" left="324" top="1470.75" width="105" height="15.75" align-x="384.75" align-y="1482" 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">f2</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">y1</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="40"/> </region> <region region-id="1159" left="30" top="1500.75" width="465.75" height="33" align-x="30" align-y="1512" 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">Запишем оператор D(x,z), задающий<sp count="2"/>правые части системы дифференциальных уравнений (здесь z</f> <f family="Arial Cyr" charset="204" size="12"> 0 </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">= y,<sp count="2"/>z</f> <f family="Arial Cyr" charset="204" size="12"> 1 </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">= y</f> <f family="Arial Cyr" charset="204" size="12">'</f> <f family="Arial Cyr" charset="204" size="12">), эквивалентной уравнению y</f> <f family="Arial Cyr" charset="204" size="12"> '' </f> <f family="Arial Cyr" charset="204" size="12">+ a*y</f> <f family="Arial Cyr" charset="204" size="12"> ' </f> <f family="Arial Cyr" charset="204" size="12">+ b*y = f(x)</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="1160" left="42" top="1567.5" width="162" height="38.25" align-x="85.5" align-y="1590" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="7dc02276-53f4-44a4-99eb-1534bd554f2c" 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<ml:real>1.4841093605960209</ml:real> <ml:real>19.99999999999995</ml:real> <ml:real>0.023252771693764905</ml:real> <ml:real>4.3369591588091794</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="50"/> </resultFormat> </math> <rendering item-idref="51"/> </region> <region region-id="1170" left="66" top="1896.75" width="361.5" height="13.5" align-x="66" align-y="1908" 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="false"> <f family="Arial Cyr" charset="204" size="12">Проверка решения в режиме анимации (~ 50 кадров) для f1(x,y,y1)</f> </text> </region> <region region-id="1208" left="72" top="1932" width="282" height="218.25" align-x="72" align-y="1932" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="52"/> <rendering item-idref="53"/> </region> <region region-id="1172" left="72" top="2184" width="387.75" height="14.25" align-x="72" align-y="2196" 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 режиме анимации используется<sp count="2"/>параметр </f> <f family="Arial Cyr" charset="204" size="12"> h </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal">.</inlineAttr> </f> </text> </region> <region region-id="1215" left="66" top="2214.75" width="429.75" height="13.5" align-x="66" align-y="2226" 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">Приведём отдельно графики функции f1</f> </text> </region> <region region-id="1209" left="54" top="2268" 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