<description/> <author>Константин Титов</author> <company/> <keywords/> <revisedBy>Titov</revisedBy> </userData> <identityInfo> <revision>24</revision> <documentID>cd4f2da9-eeab-4b7b-8b03-aa18e168ed65</documentID> <versionID>8c4191ca-b30b-482f-ac91-255a43499552</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 1"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr 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tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="List"> <blockAttr margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Indent"> <blockAttr margin-left="108" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="24" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Subtitle" base-style="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="18" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="narrow-dot" derivative="derivative" literal-subscript="large" definition="colon-equal" global-definition="triple-equal" local-definition="left-arrow" equality="bold-equal" symbolic-evaluation="right-arrow"/> <mathStyles> <mathStyle name="Variables" font-family="Arial Cyr" font-charset="204" font-size="12" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Constants" font-family="Times New Roman" font-charset="0" font-size="12" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 1" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 2" font-family="Courier New" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 3" font-family="Arial" font-charset="0" font-size="10" font-weight="bold" font-style="normal" underline="false"/> <mathStyle name="User 4" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="italic" underline="false"/> <mathStyle name="User 5" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 6" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 7" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Math Text Font" font-family="Times New Roman" font-charset="0" font-size="14" font-weight="normal" font-style="normal" underline="false"/> </mathStyles> <dimensionNames mass="mass" length="length" time="time" current="current" thermodynamic-temperature="temperature" luminous-intensity="luminosity" amount-of-substance="substance"/> <symbolics derivation-steps-style="vertical-insert" show-comments="false" evaluate-in-place="false"/> <results> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" exponential-threshold="3" imaginary-value="i" zero-threshold="15"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="28" paper-code="9" orientation="portrait" print-single-page-width="false" page-width="595.5" page-height="842.25"> <margins left="56.63622" right="16.97953" top="70.86614" bottom="70.86614"/> <header use-full-page-width="true"> <left>{\rtf1\ansi\ansicpg1251\deff0\deflang1049{\fonttbl{\f0\fswiss\fprq2\fcharset204{\*\fname Arial;}Arial CYR;}{\f1\fnil\fprq15\fcharset204{\*\fname Arial;}Arial CYR;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\f0\fs16\{p\}\par \{f\}\cf0\f1\fs18\par }</left> </header> <footer use-full-page-width="false"> <left>{\rtf1\ansi\ansicpg1251\deff0\deflang1049{\fonttbl{\f0\fnil\fprq15\fcharset204{\*\fname Arial;}Arial CYR;}} \viewkind4\uc1\pard\f0\fs18\{d\}\par }</left> <center>{\rtf1\ansi\ansicpg1251\deff0\deflang1049{\fonttbl{\f0\fnil\fprq15\fcharset0 Arial;}{\f1\fnil\fprq15\fcharset204{\*\fname Arial;}Arial CYR;}} \viewkind4\uc1\pard\qc\lang1033\f0\fs18 Titov\lang1049\f1\par }</center> <right>{\rtf1\ansi\ansicpg1251\deff0\deflang1049{\fonttbl{\f0\fnil\fprq15\fcharset204{\*\fname Arial;}Arial CYR;}} \viewkind4\uc1\pard\qr\f0\fs18\{n\}\par }</right> </footer> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="EN" UI="EN"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="true" optimize-expressions="false" exact-boolean="true" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC12" local-assignment="MC12"/> </calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor protection-level="none" view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="cm"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="false" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="1748" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="1434" left="18" top="6.75" width="125.25" height="14.25" align-x="18" align-y="18" 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"> 2.2.<sp count="2"/>Метод прогонки. </f> </text> </region> <region region-id="1418" left="12" top="36.75" width="477.75" height="40.5" align-x="12" align-y="48" 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">Это один из вариантов метода Гаусса решения системы линейных алгебраических уравнений с сильно разреженной матрицей (Бахвалов [2], стр. 552, Числ. методы), </f> <f family="Arial Cyr" charset="204" size="12">имеющей<sp count="2"/>вид:</f> </text> </region> <region region-id="1721" left="24" top="94.5" width="193.5" height="48.75" align-x="63.75" align-y="120" 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">Z</ml:id> <ml:sequence> <ml:id xml:space="preserve">i</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:sequence> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:sequence> <ml:id xml:space="preserve">i</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">j</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:parens> <ml:apply> <ml:matcol/> <ml:id xml:space="preserve">H</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> </ml:parens> <ml:sequence> <ml:id xml:space="preserve">j</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:sequence> <ml:id xml:space="preserve">j</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:sequence> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">m</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:bounds> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="2"/> </region> <region region-id="1722" left="270" top="114.75" width="66" height="15.75" align-x="300" align-y="126" 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="e8b0dbab-91f3-49fc-8155-dfd7fe778763" version-id="27e39bc8-ed23-4e09-b048-410ba96761b1" branch-id="00000000-0000-0000-0000-000000000000" revision-num="19" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\ОбАлгМетПрипДляКрЗадач.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="e8b0dbab-91f3-49fc-8155-dfd7fe778763" version-id="27e39bc8-ed23-4e09-b048-410ba96761b1" branch-id="00000000-0000-0000-0000-000000000000" revision-num="19" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\ОбАлгМетПрипДляКрЗадач.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">e7865007db0c420d374ebb936695032b</contentHash> <ml:range> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">i</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">m</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:range> </ml:provenance> </math> <rendering item-idref="3"> <element-image-map> <box left="1.5" top="0.75" width="64.5" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1723" left="348" top="114.75" width="67.5" height="15.75" align-x="381" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:range xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">k</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:range> </math> <rendering item-idref="4"/> </region> <region region-id="1423" left="12" top="162.75" width="489.75" height="165" align-x="12" align-y="174" 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 m - порядок дифференциального<sp count="2"/>уравнения; К - число дискретных точек </f> <f family="Arial Cyr" charset="204" size="12">отсчета; i - порядок производной; </f> <region region-id="1417" left="198.75" top="177.75" width="21" height="17.25" align-x="208.5" align-y="189" 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">Z</ml:id> <ml:sequence> <ml:id xml:space="preserve">i</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:sequence> </ml:apply> </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"> - дискретные значения искомого решения, записываемые в матрицу "Z"; H - кубическая матрица известных коэффициентов. </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Ниже приводится алгоритм решения для случая 3-х диагональной матрицы. Надо сказать, </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">что методы "стрельбы", "прогонки" являются частными случаями метода Гаусса. Параметры </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">дифференциального<sp count="2"/>уравнения</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>следующие: m=2,<sp count="2"/>далее см. по тексту. </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false" line-through="false">Иллюстрацию этого метода проведем на решении уравнения:</inlineAttr> </f> <region region-id="1425" left="12" top="288" width="95.25" height="15" align-x="78.75" align-y="299.25" 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:plus/> <ml:id xml:space="preserve">Z''</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:id xml:space="preserve">Z</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="6"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">,<sp count="2"/>с граничными условиями </inlineAttr> </f> <region region-id="1426" left="261.75" top="288" width="120" height="17.25" align-x="317.25" align-y="299.25" 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:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <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:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">K</ml:id> </ml:apply> </ml:apply> </ml:sequence> </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"> (здесь </inlineAttr> </f> <inlineAttr font-weight="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> Z </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">i,k</inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">,</f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="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">i=1..</f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" underline="false" line-through="false"> m </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">-1</f> </inlineAttr> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">отсутствуют - есть только </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> Z </f> <f family="Arial Cyr" charset="204" size="12"> o </f> <f family="Arial Cyr" charset="204" size="12">,k</f> <f family="Arial Cyr" charset="204" size="12">. Поэтому у </f> <f family="Arial Cyr" charset="204" size="12">Z</f> <f family="Arial Cyr" charset="204" size="12"> можно оставить один индекс, например, </f> <f family="Arial Cyr" charset="204" size="12"> k </f> <f family="Arial Cyr" charset="204" size="12">).</f> </text> </region> <region region-id="1440" left="12" top="342.75" width="210" height="13.5" align-x="12" align-y="354" 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">Перейдем к дискретным переменным:</f> </text> </region> <region region-id="1450" left="234" top="342.75" width="45" height="15.75" align-x="264" align-y="354" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:range xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">j</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:id xml:space="preserve">K</ml:id> </ml:range> </math> <rendering item-idref="8"/> </region> <region region-id="1582" left="294" top="342.75" width="34.5" height="17.25" align-x="312" align-y="354" 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:real>0</ml:real> </ml:apply> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </math> <rendering item-idref="9"/> </region> <region region-id="1583" left="348" top="342.75" width="59.25" height="17.25" align-x="363.75" align-y="354" 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">j</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">j</ml:id> <ml:id xml:space="preserve">h</ml:id> </ml:apply> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="10"/> </region> <region region-id="1584" left="432" top="342.75" width="36" height="17.25" align-x="451.5" align-y="354" 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">K</ml:id> </ml:apply> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </math> <rendering item-idref="11"/> </region> <region region-id="1456" left="18" top="379.5" width="486.75" height="142.5" align-x="18" align-y="390" 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 запишем рекуррентные формулы вычисления<sp count="2"/>решения<sp count="3"/>исходного<sp count="2"/>дифференци- ального уравнения, представленного в разностном виде: </f> <region region-id="122" left="18" top="407.25" width="189.75" height="39.75" align-x="174.75" align-y="428.25" 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:plus/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </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:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">P</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </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"> ,<sp count="3"/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">Выразим из этого уравнения : </f> <region region-id="1457" left="18" top="447.75" width="195.75" height="22.5" align-x="47.25" align-y="464.25" 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">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="13"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> .<sp count="2"/>(здесь<sp count="2"/>j=1, 2, ...). Далее найдём</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> функциональную зависимость F: </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="1586" left="107.25" top="471" width="96" height="17.25" align-x="124.5" align-y="482.25" 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">Z</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">F</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:sequence> </ml:apply> </ml:apply> </math> <rendering item-idref="14"/> </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="10"> <inlineAttr font-weight="normal" underline="false" line-through="false">Примечание</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Выразить Z</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> j </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> <f family="Arial Cyr" charset="204" size="10">как </f> <region region-id="1585" left="153" top="489" width="96" height="17.25" align-x="170.25" align-y="500.25" 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">Z</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">F</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:sequence> </ml:apply> </ml:apply> </math> <rendering item-idref="15"/> </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="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">можно в общем случае только<sp count="2"/>для линейных дифференциальных уравнений. </inlineAttr> </f> </text> </region> <region region-id="1696" left="18" top="538.5" width="238.5" height="40.5" align-x="35.25" align-y="558" 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">Z</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">j</ml:id> </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:parens> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="16"/> </region> <region region-id="1695" left="294" top="546.75" width="60" height="15.75" align-x="304.5" align-y="558" 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">j</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1..</ml:real> <ml:id xml:space="preserve">K</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="17"/> </region> <region region-id="1694" left="444" top="546.75" width="17.25" height="15.75" align-x="451.5" align-y="558" 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="1698" left="18" top="594" width="475.5" height="30.75" align-x="18" align-y="606" 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 (1) задает СЛАУ из (</f> <f family="Arial Cyr" charset="204" size="12"> К </f> <f family="Arial Cyr" charset="204" size="12">-1) уравнений и </f> <f family="Arial Cyr" charset="204" size="12">(</f> <f family="Arial Cyr" charset="204" size="12"> К </f> <f family="Arial Cyr" charset="204" size="12">-1) неизвестных, из которых надо определить (Z</f> <f family="Arial Cyr" charset="204" size="12"> 1 </f> <f family="Arial Cyr" charset="204" size="12">, ... ,Z</f> <f family="Arial Cyr" charset="204" size="12">K-1</f> <f family="Arial Cyr" charset="204" size="12">), а<sp count="2"/>Z</f> <f family="Arial Cyr" charset="204" size="12"> 0 </f> <f family="Arial Cyr" charset="204" size="12"> и Z</f> <f family="Arial Cyr" charset="204" size="12"> K </f> <f family="Arial Cyr" charset="204" size="12"> - известны из граничных условий.</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="1647" left="450" top="648.75" width="17.25" height="15.75" align-x="457.5" align-y="660" 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="19"/> </region> <region region-id="1593" left="24" top="654.75" width="119.25" height="13.5" align-x="24" align-y="666" 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">Введём обозначения:</f> </text> </region> <region region-id="1595" left="174" top="646.5" width="78.75" height="40.5" align-x="193.5" align-y="666" 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">Q</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="20"/> </region> <region region-id="1594" left="294" top="649.5" width="112.5" height="22.5" align-x="312" align-y="666" 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">φ</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">j</ml:id> </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:parens> </ml:apply> </ml:apply> </math> <rendering item-idref="21"/> </region> <region region-id="1650" left="24" top="708.75" width="81.75" height="13.5" align-x="24" 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">Тогда получим:</f> </text> </region> <region region-id="1651" left="132" top="703.5" width="163.5" height="22.5" align-x="149.25" 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:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">j</ml:id> </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:parens> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="22"/> </region> <region region-id="1653" left="456" top="708.75" width="17.25" height="15.75" align-x="463.5" 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:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>3</ml:real> </ml:parens> </math> <rendering item-idref="23"/> </region> <region region-id="1707" left="24" top="750.75" width="354" height="23.25" align-x="24" align-y="768" 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">Из (3) для j=1 следует: </f> <region region-id="1708" left="150.75" top="751.5" width="226.5" height="22.5" align-x="310.5" align-y="768" 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:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>1</ml:real> </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:parens> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="24"/> </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="1596" left="24" top="785.25" width="487.5" height="84.75" align-x="24" 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">Так как Z</f> <f family="Arial Cyr" charset="204" size="12"> o </f> <f family="Arial Cyr" charset="204" size="12"> известно из граничных условий, то, следовательно, известно и </f> <region region-id="1597" left="432" top="786" width="13.5" height="18" align-x="438" 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:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="25"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Поэтому </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(3) для j=1 можно записать как </inlineAttr> </f> <region region-id="1598" left="196.5" top="809.25" width="64.5" height="17.25" align-x="216" align-y="820.5" 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:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">F</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </math> <rendering item-idref="26"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Эта зависимость определяет предыдущее</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">значение Z через последующее пока неизвестное. Нам же надо найти всё множество значений {Z</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">j</inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">}, j=1,2,...,K-1. Поступая как в предыдущем случае, найдём зависимость F</f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> j </inlineAttr> </f> <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">для j=2, записав формулу (3): </inlineAttr> </f> </text> </region> <region region-id="1617" left="48" top="894" width="86.25" height="18" align-x="67.5" 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:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="27"/> </region> <region region-id="1616" left="150" top="894.75" width="33.75" height="13.5" align-x="150" 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">Здесь</f> </text> </region> <region region-id="1615" left="192" top="889.5" width="109.5" height="22.5" align-x="212.25" 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:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>2</ml:real> </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:parens> </ml:apply> </ml:apply> </math> <rendering item-idref="28"/> </region> <region region-id="1612" left="36" top="929.25" width="468" height="18.75" align-x="36" align-y="942" 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 в выражение для </f> <region region-id="1709" left="199.5" top="930" width="13.5" height="18" align-x="205.5" align-y="942" 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">φ</ml:id> <ml:real>2</ml:real> </ml:apply> </math> <rendering item-idref="29"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> найденное ранее </inlineAttr> </f> <region region-id="1710" left="316.5" top="930.75" width="12.75" height="17.25" align-x="321.75" align-y="942" 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">Z</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="30"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> и запишем</inlineAttr> </f> </text> </region> <region region-id="1643" left="36" top="976.5" width="345" height="40.5" align-x="55.5" align-y="996" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="true" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>1</ml:real> </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:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>2</ml:real> </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:parens> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="31"/> </region> <region region-id="1669" left="36" top="1032.75" width="464.25" height="52.5" align-x="36" align-y="1044" 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">Последнее уравнение линейно связывает Z</f> <f family="Arial Cyr" charset="204" size="12"> 2 </f> <f family="Arial Cyr" charset="204" size="12"> и Z</f> <f family="Arial Cyr" charset="204" size="12"> 3 </f> <f family="Arial Cyr" charset="204" size="12"> и позволяет выразить<sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12">Z</f> <f family="Arial Cyr" charset="204" size="12"> 2 </f> <f family="Arial Cyr" charset="204" size="12"> <sp count="3"/>через </f> <f family="Arial Cyr" charset="204" size="12">Z</f> <f family="Arial Cyr" charset="204" size="12">3</f> <f family="Arial Cyr" charset="204" size="12">, то есть получить зависимость </f> <region region-id="1620" left="222.75" top="1050.75" width="64.5" height="17.25" align-x="242.25" align-y="1062" 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">Z</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">F</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:parens> </ml:apply> </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">. Теоретически эту зависимость </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">найти </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">можно так</inlineAttr> </f> </text> </region> <region region-id="1639" left="42" top="1098.75" width="30.75" height="15" align-x="56.25" align-y="1110" 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">Given</ml:id> </math> <rendering item-idref="33"/> </region> <region region-id="1644" left="48" top="1123.5" width="258" height="22.5" align-x="67.5" align-y="1140" 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">z2</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">q2</ml:id> <ml:id xml:space="preserve">z3</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">q2</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">q1</ml:id> <ml:id xml:space="preserve">z2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">q1</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">z0</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>1</ml:real> </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:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>2</ml:real> </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:apply> </ml:apply> </math> <rendering item-idref="34"/> </region> <region region-id="1645" left="54" top="1159.5" width="379.5" height="22.5" align-x="108" align-y="1176" 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:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:id xml:space="preserve">z2</ml:id> </ml:apply> <ml:symResult> <ml:apply> <ml:id xml:space="preserve">RootOf</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">_Z</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">q2</ml:id> <ml:id xml:space="preserve">z3</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">q2</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">q1</ml:id> <ml:id xml:space="preserve">_Z</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">q1</ml:id> <ml:id xml:space="preserve">z0</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">q1</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>1</ml:real> </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:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>2</ml:real> </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:apply> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="35"/> </region> <region region-id="1699" left="36" top="1194.75" width="471" height="25.5" align-x="36" align-y="1206" 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">. Однако определение z2 через RootOf практического значения не находит. В Maple</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="10">это сделать </f> <f family="Arial Cyr" charset="204" size="10">проще, используя опцию </f> <f family="Arial Cyr" charset="204" size="10"> solve </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-style="normal">или</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <sp/> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-style="normal">subs и simplify</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-style="normal">.</inlineAttr> </f> </text> </region> <region region-id="1654" left="42" top="1236.75" width="403.5" height="16.5" align-x="42" align-y="1248" 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">Приводя подобные члены и относя Z</f> <f family="Arial Cyr" charset="204" size="12"> 2 </f> <f family="Arial Cyr" charset="204" size="12"> в левую часть уравнения, получим: </f> </text> </region> <region region-id="1661" left="396" top="1272.75" width="17.25" height="15.75" align-x="403.5" align-y="1284" 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="36"/> </region> <region region-id="1655" left="54" top="1269" width="236.25" height="36.75" align-x="73.5" 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:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>2</ml:real> </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:parens> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="37"/> </region> <region region-id="1656" left="48" top="1326.75" width="155.25" height="13.5" align-x="48" align-y="1338" 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">Вновь введём обозначения:</f> </text> </region> <region region-id="1657" left="228" top="1317" width="87" height="36.75" align-x="249.75" align-y="1338" 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">C</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="38"/> </region> <region region-id="1658" left="342" top="1317" width="151.5" height="36.75" align-x="362.25" align-y="1338" 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">φ</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>2</ml:real> </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:parens> </ml:apply> </ml:apply> </math> <rendering item-idref="39"/> </region> <region region-id="1659" left="48" top="1367.25" width="399.75" height="23.25" align-x="48" align-y="1380" 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<sp count="2"/>С</f> <f family="Arial Cyr" charset="204" size="12"> 2 </f> <f family="Arial Cyr" charset="204" size="12"> и </f> <region region-id="1660" left="100.5" top="1368" width="13.5" height="18" align-x="106.5" align-y="1380" 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">φ</ml:id> <ml:real>2</ml:real> </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"> по-прежнему известны. Перепишем (4) в следующем виде</inlineAttr> </f> </text> </region> <region region-id="1664" left="60" top="1416" width="86.25" height="18" align-x="79.5" align-y="1428" 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">Z</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="41"/> </region> <region region-id="1665" left="336" top="1416.75" width="17.25" height="15.75" align-x="343.5" align-y="1428" 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="42"/> </region> <region region-id="1673" left="24" top="1446.75" width="467.25" height="30" align-x="24" align-y="1458" 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">Продолжим этот процесс исключения переменных дальше. </f> <f family="Arial Cyr" charset="204" size="12">Изменяя j=1..K-1 и выражая всякий раз Z</f> <f family="Arial Cyr" charset="204" size="12"> j </f> <f family="Arial Cyr" charset="204" size="12">через</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>Z</f> <f family="Arial Cyr" charset="204" size="12"> j+1 </f> <f family="Arial Cyr" charset="204" size="12">, дойдем, наконец, до уравнения:</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="1676" left="114" top="1494" width="101.25" height="18" align-x="134.25" align-y="1506" 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">Z</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </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> </math> <rendering item-idref="43"/> </region> <region region-id="1677" left="354" top="1494.75" width="17.25" height="15.75" align-x="361.5" align-y="1506" 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="44"/> </region> <region region-id="1459" left="24" top="1529.25" width="479.25" height="121.5" align-x="24" align-y="1542" 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"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Здесь </inlineAttr> </f> <region region-id="1466" left="60" top="1530.75" width="15.75" height="17.25" align-x="66.75" align-y="1542" 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">C</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="45"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> и</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/> </f> <region region-id="1467" left="92.25" top="1530" width="14.25" height="18" align-x="98.25" align-y="1542" 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">φ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="46"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> -<sp count="2"/>известные<sp count="2"/>коэффициенты. </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">Подставим (6) в (n+1)-е уравнение (1)</f> <f family="Arial Cyr" charset="204" size="12">или (3). Вновь разрешая его: </f> <region region-id="1576" left="186" top="1548.75" width="217.5" height="22.5" align-x="218.25" align-y="1565.25" 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">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</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">f</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</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:parens> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="47"/> </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">или,<sp count="65"/>подставляя в последнее вместо<sp count="2"/>Z</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">выражение (6), получим</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="1575" left="24" top="1588.5" width="307.5" height="22.5" align-x="56.25" align-y="1605" 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">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <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:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</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:parens> </ml:apply> </ml:apply> </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">. Приведём подобные члены</inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">и</f> </inlineAttr> <f family="Times New Roman 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">н</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">айдем:<sp count="2"/> </inlineAttr> </f> <region region-id="1570" left="84.75" top="1611.75" width="299.25" height="22.5" align-x="198" align-y="1628.25" 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:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <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:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</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:parens> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="49"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> . Левую и правую части уравнения поделим на коэффициент при Z</inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">n+1</f> </inlineAttr> <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="1731" left="12" top="1668.75" width="450.75" height="59.25" align-x="12" align-y="1680" 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">Тогда выразим Z</f> <f family="Arial Cyr" charset="204" size="12"> n+1 </f> <f family="Arial Cyr" charset="204" size="12"> :</f> <region region-id="1571" left="12" top="1686.75" width="234" height="42" align-x="44.25" align-y="1713" 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">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <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:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</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:parens> </ml:apply> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="50"/> </region> <f family="Arial Cyr" charset="204" size="12"> , где (см.(2))<sp count="2"/> </f> <region region-id="1572" left="315.75" top="1693.5" width="105.75" height="40.5" align-x="350.25" align-y="1713" 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">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="51"/> </region> <f family="Arial Cyr" charset="204" size="12"> .</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="1732" left="12" top="1746.75" width="468" height="32.25" align-x="12" align-y="1758" 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 итоге </f> <f family="Arial Cyr" charset="204" size="12">получим:</f> <region region-id="1463" left="12" top="1761.75" width="137.25" height="18" align-x="44.25" align-y="1773.75" 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">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="52"/> </region> <f family="Arial Cyr" charset="204" size="12"> ,<sp count="2"/>где </f> <f family="Arial Cyr" charset="204" size="12"> n = 0,1, ..., (K-2).</f> </text> </region> <region region-id="1730" left="372" top="1752.75" width="17.25" height="15.75" align-x="379.5" align-y="1764" 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="53"/> </region> <region region-id="1734" left="18" top="1794.75" width="455.25" height="56.25" align-x="18" align-y="1806" 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">Коэффициенты в (7) определяются по тождественным реккурентным формулам</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="1468" left="21" top="1809.75" width="233.25" height="42" align-x="175.5" align-y="1830.75" 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:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="54"/> </region> <f family="Arial Cyr" charset="204" size="12">,<sp count="2"/> </f> <region region-id="1480" left="258.75" top="1814.25" width="149.25" height="22.5" align-x="291.75" align-y="1830.75" 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">φ</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <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:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</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:parens> </ml:apply> </ml:apply> </math> <rendering item-idref="55"/> </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"> <sp count="9"/>(8)</f> </text> </region> <region region-id="1737" left="24" top="1860" width="229.5" height="18.75" align-x="24" align-y="1872" 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">Причём следует считать, что C</f> <f family="Arial Cyr" charset="204" size="12"> 0 </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr>=0, </inlineAttr> </f> <f family="Symbol" charset="2" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">f</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> 0 </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr>=0.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr> <sp count="2"/> </inlineAttr> </f> </text> </region> <region region-id="1733" left="24" top="1896" width="471.75" height="73.5" align-x="24" 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="true"> <f family="Arial Cyr" charset="204" size="12">Исходя из (3) и общей формулы (7), которая при </f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">=0 должна сводиться к (3), при </f> <f family="Arial Cyr" charset="204" size="12">изме</f> <f family="Arial Cyr" charset="204" size="12">нении индекса </f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">=0,1,... следует положить </f> <region region-id="1713" left="283.5" top="1911.75" width="45.75" height="17.25" align-x="305.25" align-y="1923" 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">C</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="56"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, если </inlineAttr> </f> <region region-id="1714" left="364.5" top="1911.75" width="37.5" height="17.25" align-x="386.25" align-y="1923" 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">C</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="57"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. А</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> из равен-</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">ства </inlineAttr> </f> <region region-id="1715" left="51" top="1932.75" width="110.25" height="22.5" align-x="71.25" align-y="1949.25" 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">φ</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>1</ml:real> </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:parens> </ml:apply> </ml:apply> </math> <rendering item-idref="58"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> следует </inlineAttr> </f> <region region-id="1716" left="209.25" top="1937.25" width="42" height="18" align-x="229.5" align-y="1949.25" 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">φ</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="59"/> </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">Здесь </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="1688" left="296.25" top="1929.75" width="108.75" height="40.5" align-x="330.75" align-y="1949.25" 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">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </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"> (см. (2))</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="1552" left="24" top="1980.75" width="491.25" height="116.25" align-x="24" align-y="1992" 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, коэффициенты уравнений (7), связывающих последующие и преды-</f> <f family="Arial Cyr" charset="204" size="12">дущие значения </f> <f family="Arial Cyr" charset="204" size="12"> (Z</f> <f family="Arial Cyr" charset="204" size="12"> n<sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12">и</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="3"/> </f> <f family="Arial Cyr" charset="204" size="12">Z</f> <f family="Arial Cyr" charset="204" size="12"> n+1 </f> <f family="Arial Cyr" charset="204" size="12">)</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">, можно определять из рекуррентных соотношений (8) </f> <f family="Arial Cyr" charset="204" size="12">при начальных значен</f> <f family="Arial Cyr" charset="204" size="12">иях для: </f> <region region-id="1483" left="197.25" top="2013" width="37.5" height="17.25" align-x="219" align-y="2024.25" 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">C</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>0</ml:real> </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"> <sp/> </inlineAttr> </f> <region region-id="1484" left="237.75" top="2012.25" width="42" height="18" align-x="258" align-y="2024.25" 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">φ</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="62"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Так<sp count="2"/>как<sp count="2"/>Z</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">K<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">известно, то после нахож-</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">де</inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">ния всех коэффициентов C</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"> , </inlineAttr> </f> <region region-id="1485" left="204" top="2035.5" width="14.25" height="18" align-x="210" align-y="2047.5" 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:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="63"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> можно последовательно определять<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/> </inlineAttr> </f> <region region-id="1486" left="27" top="2059.5" width="63.75" height="17.25" align-x="74.25" align-y="2070.75" 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:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:real>....</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:sequence> </math> <rendering item-idref="64"/> </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">из (6). Процесс вычисления коэффициентов </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12">C</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12"> , </f> <region region-id="1516" left="367.5" top="2058.75" width="14.25" height="18" align-x="373.5" align-y="2070.75" 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">φ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="65"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> принято называть </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr underline="false" line-through="false">прямым<sp count="2"/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr underline="false" line-through="false"> ходом </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> прогонки, а п</f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12">роцесс вычисления </f> <f family="Arial Cyr" charset="204" size="12">Z</f> <f family="Arial Cyr" charset="204" size="12"> n<sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12">- </f> <f family="Arial Cyr" charset="204" size="12">обратным ходом </f> <f family="Arial Cyr" charset="204" size="12">прогонки.</f> </text> </region> <region region-id="1738" left="24" top="2130.75" width="485.25" height="51" align-x="24" align-y="2148" 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">Пример. Рассмотрим на примере решения уравнения </f> <region region-id="49" left="329.25" top="2131.5" width="91.5" height="20.25" align-x="391.5" align-y="2148" 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:id xml:space="preserve">y''</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:id xml:space="preserve">y</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="66"/> </region> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>с граничными </f> <f family="Arial Cyr" charset="204" size="12">условиями: </f> <region region-id="1553" left="90" top="2152.5" width="45.75" height="15.75" align-x="120" align-y="2163.75" 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:id xml:space="preserve">y</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>1</ml:real> </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">,<sp count="2"/> </inlineAttr> </f> <region region-id="1554" left="145.5" top="2152.5" width="45.75" height="15.75" align-x="175.5" align-y="2163.75" 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:id xml:space="preserve">y</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:real>2</ml:real> </ml:apply> </math> <rendering item-idref="68"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>работу этого метода </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">(следует заметить, что не для любых краевых условий подобные задачи имеют решение).</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="1556" left="24" top="2202.75" width="478.5" height="13.5" align-x="36.75" align-y="2214" 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"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Точное решение этого уравнения, полученное ранее,<sp count="2"/>при p(x)=1 </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">есть</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="1431" left="36" top="2230.5" width="306" height="33.75" align-x="66.75" align-y="2250" 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="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.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">d24946bdc5ae5d1781c61009d188e828</contentHash> <ml:define> <ml:function> <ml:id xml:space="preserve">yt</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:real>-4</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="69"> <element-image-map> <box left="1.5" top="0.75" width="304.5" height="32.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1432" left="360" top="2238.75" width="56.25" height="15.75" align-x="393" align-y="2250" 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:provenance expr-id="1"> <originRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.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">72f877ffa76c567a47fae3ce36224632</contentHash> <ml:apply> <ml:id xml:space="preserve">yt</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:provenance> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="70"> <element-image-map> <box left="1.5" top="0.75" width="24.75" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1433" left="438" top="2238.75" width="56.25" height="15.75" align-x="471" align-y="2250" 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:provenance expr-id="1"> <originRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.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">9e46a6caabef99fad916a5d4b9059406</contentHash> <ml:apply> <ml:id xml:space="preserve">yt</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:provenance> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>2</ml:real> </result> </ml:eval> </math> <rendering item-idref="71"> <element-image-map> <box left="1.5" top="0.75" width="24.75" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1528" left="18" top="2292.75" width="127.5" height="13.5" align-x="18" align-y="2304" 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">Введем обозначения:</f> </text> </region> <region region-id="1739" left="162" top="2287.5" width="57.75" height="20.25" align-x="189.75" align-y="2304" 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="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.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">51727d0ea280e42932ac19c84d9aef9c</contentHash> <ml:define> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="72"> <element-image-map> <box left="1.5" top="0.75" width="56.25" height="18.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1527" left="18" top="2322" width="93.75" height="16.5" align-x="18" align-y="2334" 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">Дано:</f> <region region-id="1424" left="49.5" top="2322.75" width="48.75" height="15.75" align-x="81.75" align-y="2334" 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">P</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="73"/> </region> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="1557" left="114" top="2322.75" width="89.25" height="15.75" align-x="131.25" align-y="2334" 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:real>5</ml:real> <ml:id xml:space="preserve">FRAME</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="74"/> </region> <region region-id="1536" left="216" top="2322.75" width="47.25" height="15.75" align-x="228" align-y="2334" 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="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.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">0b580a5f0cd970190c98a1f010237f7b</contentHash> <ml:define> <ml:id xml:space="preserve">j</ml:id> <ml:range> <ml:real>0</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:range> </ml:define> </ml:provenance> </math> <rendering item-idref="75"> <element-image-map> <box left="1.5" top="0.75" width="45.75" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1537" left="282" top="2322.75" width="32.25" height="15.75" align-x="297.75" align-y="2334" 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="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.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">a965492222e0660fecda95685c52e14b</contentHash> <ml:define> <ml:id xml:space="preserve">a</ml:id> <ml:real>0</ml:real> </ml:define> </ml:provenance> </math> <rendering item-idref="76"> <element-image-map> <box left="1.5" top="0.75" width="30.75" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1538" left="324" top="2322.75" width="32.25" height="15.75" align-x="339.75" align-y="2334" 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="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.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">8478bff1e34ef83244d30da3d4617af0</contentHash> <ml:define> <ml:id xml:space="preserve">b</ml:id> <ml:real>4</ml:real> </ml:define> </ml:provenance> </math> <rendering item-idref="77"> <element-image-map> <box left="1.5" top="0.75" width="30.75" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1539" left="366" top="2315.25" width="55.5" height="32.25" align-x="381" align-y="2334" 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="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.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">895772ad97b5f283362e8ce2822c1c63</contentHash> <ml:define> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="78"> <element-image-map> <box left="1.5" top="0.75" width="54" height="30.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1540" left="438" top="2322.75" width="45.75" height="15.75" align-x="451.5" align-y="2334" 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:provenance expr-id="1"> <originRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.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">e7bc9de7c6f0c5330ae91971ef8d3b69</contentHash> <ml:id xml:space="preserve">h</ml:id> </ml:provenance> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.8</ml:real> </result> </ml:eval> </math> <rendering item-idref="79"> <element-image-map> <box left="1.5" top="0.75" width="5.25" height="13.5" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="67" left="12" top="2358.75" width="210" height="13.5" align-x="12" align-y="2370" 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">Перейдем к дискретным переменным:</f> </text> </region> <region region-id="1702" left="240" top="2358.75" width="36.75" height="17.25" align-x="259.5" align-y="2370" 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="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.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">b45f53bc7cc59dfe49f4486d93bc6b58</contentHash> <ml:define> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:id xml:space="preserve">a</ml:id> </ml:define> </ml:provenance> </math> <rendering item-idref="80"> <element-image-map> <box left="1.5" top="0.75" width="35.25" height="15.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1703" left="312" top="2358.75" width="65.25" height="17.25" align-x="329.25" align-y="2370" 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">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">j</ml:id> <ml:id xml:space="preserve">h</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="81"/> </region> <region region-id="1704" left="396" top="2358.75" width="42.75" height="17.25" align-x="415.5" align-y="2370" 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">x</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>4</ml:real> </result> </ml:eval> </math> <rendering item-idref="82"/> </region> <region region-id="71" left="12" top="2394.75" width="109.5" height="13.5" align-x="12" align-y="2406" 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="72" left="138" top="2394.75" width="38.25" height="17.25" align-x="159.75" 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:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Y</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="83"/> </region> <region region-id="73" left="198" top="2394.75" width="39.75" height="17.25" align-x="221.25" 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:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:define> </math> <rendering item-idref="84"/> </region> <region region-id="1499" left="264" top="2394.75" width="39.75" height="17.25" align-x="287.25" 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:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="85"/> </region> <region region-id="1500" left="330" top="2394" width="45" height="18" align-x="351.75" 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:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:real>0</ml:real> </ml:apply> <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="86"/> </region> <region region-id="74" left="12" top="2424" width="491.25" height="49.5" align-x="12" align-y="2436" 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 введены обозначения: </f> <region region-id="97" left="222.75" top="2424.75" width="11.25" height="17.25" align-x="227.25" align-y="2436" 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">Y</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </math> <rendering item-idref="87"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> - дискретные значения<sp count="2"/>решения<sp count="2"/>дифференциального<sp count="2"/>уравнения;<sp count="2"/> </inlineAttr> </f> <region region-id="98" left="204" top="2442.75" width="18" height="17.25" align-x="212.25" align-y="2454" 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">Y1</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </math> <rendering item-idref="88"/> </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">дискретные значения 1-й производной<sp count="2"/>решения<sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12">дифференциального </f> <f family="Arial Cyr" charset="204" size="12"> уравнения. </f> <f family="Arial Cyr" charset="204" size="12">Согласно формулам (7) и (8) будем иметь:</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="1487" left="36" top="2496.75" width="58.5" height="17.25" align-x="56.25" align-y="2508" 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="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">P</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="89"/> </region> <region region-id="1488" left="120" top="2496.75" width="49.5" height="17.25" align-x="135.75" align-y="2508" 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="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="90"/> </region> <region region-id="1489" left="198" top="2496.75" width="44.25" height="17.25" align-x="219" align-y="2508" 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">P</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="91"/> </region> <region region-id="1490" left="264" top="2496.75" width="62.25" height="17.25" align-x="282" align-y="2508" 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">f</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.018315638888734182</ml:real> </result> </ml:eval> </math> <rendering item-idref="92"/> </region> <region region-id="1496" left="348" top="2496.75" width="42.75" height="17.25" align-x="367.5" align-y="2508" 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">x</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>4</ml:real> </result> </ml:eval> </math> <rendering item-idref="93"/> </region> <region region-id="1497" left="30" top="2532.75" width="189.75" height="81.75" align-x="48" align-y="2544" 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">C</ml:id> <ml:program> <ml:for> <ml:id xml:space="preserve">j</ml:id> <ml:range> <ml:real>0</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:range> <ml:localDefine> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:localDefine> </ml:for> <ml:id xml:space="preserve">C</ml:id> </ml:program> </ml:define> </math> <rendering item-idref="94"/> </region> <region region-id="1506" left="288" top="2538" width="197.25" height="66" align-x="304.5" align-y="2550" 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">φ</ml:id> <ml:program> <ml:for> <ml:id xml:space="preserve">j</ml:id> <ml:range> <ml:real>0</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:range> <ml:localDefine> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</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:parens> </ml:apply> </ml:localDefine> </ml:for> <ml:id xml:space="preserve">φ</ml:id> </ml:program> </ml:define> </math> <rendering item-idref="95"/> </region> <region region-id="1740" left="24" top="2648.25" width="474" height="72" align-x="24" align-y="2658" 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">. Проверка этих алгоритмов сделана в Maple: файл "МетПрогонки_приложение.mws"</f> <f family="Arial Cyr" charset="204" size="12">После нахождения всех коэффициентов C</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12"> , </f> <region region-id="1517" left="276" top="2661" width="14.25" height="18" align-x="282" align-y="2673" 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">φ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="96"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, записанных в векторы C и </inlineAttr> </f> <f family="Symbol" charset="2" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">f</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> можно последовательно определять<sp count="3"/> </f> <region region-id="1518" left="197.25" top="2684.25" width="65.25" height="17.25" align-x="245.25" align-y="2695.5" 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:indexer/> <ml:id xml:space="preserve">Y</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:real>....</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Y</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:sequence> </math> <rendering item-idref="97"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">,<sp count="2"/>таким образом:</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="1558" left="362.25" top="2684.25" width="66.75" height="15.75" align-x="374.25" align-y="2695.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i</ml:id> <ml:range> <ml:real>0</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="98"/> </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"> <sp count="3"/> </inlineAttr> </f> <region region-id="1559" left="24" top="2702.25" width="168" height="18" align-x="68.25" 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:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Y</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">i</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">i</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Y</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">i</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="99"/> </region> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="1742" left="48" top="2832" width="361.5" height="223.5" align-x="48" align-y="2832" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="100"/> <rendering item-idref="101"/> </region> <region region-id="1744" left="438" top="2910.75" width="45.75" height="15.75" align-x="451.5" align-y="2922" 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">h</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.8</ml:real> </result> </ml:eval> </math> <rendering item-idref="102"/> </region> <region region-id="1746" left="444" top="2946.75" width="43.5" height="17.25" align-x="464.25" align-y="2958" 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:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="103"/> </region> <region region-id="1747" left="444" top="2976.75" width="45" height="17.25" align-x="465.75" align-y="2988" 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">N</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>2</ml:real> </result> </ml:eval> </math> <rendering item-idref="104"/> </region> <region region-id="1748" left="42" top="3114.75" width="441" height="13.5" align-x="42" align-y="3126" 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">Рис. 1. </f> <f family="Arial Cyr" charset="204" size="12">Возможна анимация </f> <f family="Arial Cyr" charset="204" size="12">графика.(50 кадров).</f> </text> </region> <region region-id="1706" left="42" top="3150.75" width="221.25" height="13.5" align-x="42" align-y="3162" 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">Точность решения зависит только от "h".</f> </text> </region> <region region-id="1545" left="30" top="3186" width="478.5" height="59.25" align-x="30" 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"> Упражнение . </f> <f family="Arial Cyr" charset="204" size="12">Решить численно </f> <f family="Arial Cyr" charset="204" size="12"> дифференциальное уравнение </f> <region region-id="1724" left="384.75" top="3186.75" width="95.25" height="15" align-x="451.5" align-y="3198" 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:id xml:space="preserve">Z''</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:id xml:space="preserve">Z</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="105"/> </region> <f family="Arial Cyr" charset="204" size="12">для </f> <f family="Arial Cyr" charset="204" size="12">различных p(x):<sp count="2"/>x</f> <f family="Arial Cyr" charset="204" size="12"> 2 </f> <f family="Arial Cyr" charset="204" size="12">,<sp count="2"/>x</f> <f family="Arial Cyr" charset="204" size="12"> 3 </f> <f family="Arial Cyr" charset="204" size="12">,<sp count="2"/>sin(x)<sp count="2"/>и др.<sp count="3"/>и<sp count="2"/>f(x): sin(x),<sp count="2"/>cos(x)<sp count="2"/>и др.</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">Запишем краевые условия: y(0)=1,<sp count="2"/>y(4)=2. 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fractional-unit-exponent="false"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="28" paper-code="9" orientation="portrait" print-single-page-width="false" page-width="595.5" page-height="842.25"> <margins left="56.63622" right="16.97953" top="70.86614" bottom="70.86614"/> <header use-full-page-width="true"> <left>{\rtf1\ansi\ansicpg1251\deff0\deflang1049{\fonttbl{\f0\fswiss\fprq2\fcharset204{\*\fname Arial;}Arial CYR;}{\f1\fnil\fprq15\fcharset204{\*\fname Arial;}Arial CYR;}} {\colortbl ;\red0\green0\blue0;} \viewkind4\uc1\pard\cf1\f0\fs16\{p\}\par \{f\}\cf0\f1\fs18\par }</left> </header> <footer use-full-page-width="false"> <left>{\rtf1\ansi\ansicpg1251\deff0\deflang1049{\fonttbl{\f0\fnil\fprq15\fcharset204{\*\fname Arial;}Arial CYR;}} \viewkind4\uc1\pard\f0\fs18\{d\}\par }</left> <center>{\rtf1\ansi\ansicpg1251\deff0\deflang1049{\fonttbl{\f0\fnil\fprq15\fcharset0 Arial;}{\f1\fnil\fprq15\fcharset204{\*\fname Arial;}Arial CYR;}} \viewkind4\uc1\pard\qc\lang1033\f0\fs18 Titov\lang1049\f1\par }</center> <right>{\rtf1\ansi\ansicpg1251\deff0\deflang1049{\fonttbl{\f0\fnil\fprq15\fcharset204{\*\fname Arial;}Arial CYR;}} \viewkind4\uc1\pard\qr\f0\fs18\{n\}\par }</right> </footer> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="EN" UI="EN"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="true" optimize-expressions="false" exact-boolean="true" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC12" local-assignment="MC12"/> </calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor protection-level="none" view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="cm"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="false" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="1748" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="1434" left="18" top="6.75" width="125.25" height="14.25" align-x="18" align-y="18" 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"> 2.2.<sp count="2"/>Метод прогонки. </f> </text> </region> <region region-id="1418" left="12" top="36.75" width="477.75" height="40.5" align-x="12" align-y="48" 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">Это один из вариантов метода Гаусса решения системы линейных алгебраических уравнений с сильно разреженной матрицей (Бахвалов [2], стр. 552, Числ. методы), </f> <f family="Arial Cyr" charset="204" size="12">имеющей<sp count="2"/>вид:</f> </text> </region> <region region-id="1721" left="24" top="94.5" width="193.5" height="48.75" align-x="63.75" align-y="120" 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">Z</ml:id> <ml:sequence> <ml:id xml:space="preserve">i</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:sequence> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:sequence> <ml:id xml:space="preserve">i</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">j</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:parens> <ml:apply> <ml:matcol/> <ml:id xml:space="preserve">H</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> </ml:parens> <ml:sequence> <ml:id xml:space="preserve">j</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:sequence> <ml:id xml:space="preserve">j</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:sequence> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">m</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:bounds> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="2"/> </region> <region region-id="1722" left="270" top="114.75" width="66" height="15.75" align-x="300" align-y="126" 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="e8b0dbab-91f3-49fc-8155-dfd7fe778763" version-id="27e39bc8-ed23-4e09-b048-410ba96761b1" branch-id="00000000-0000-0000-0000-000000000000" revision-num="19" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\ОбАлгМетПрипДляКрЗадач.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="e8b0dbab-91f3-49fc-8155-dfd7fe778763" version-id="27e39bc8-ed23-4e09-b048-410ba96761b1" branch-id="00000000-0000-0000-0000-000000000000" revision-num="19" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\ОбАлгМетПрипДляКрЗадач.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">e7865007db0c420d374ebb936695032b</contentHash> <ml:range> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">i</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">m</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:range> </ml:provenance> </math> <rendering item-idref="3"> <element-image-map> <box left="1.5" top="0.75" width="64.5" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1723" left="348" top="114.75" width="67.5" height="15.75" align-x="381" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:range xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">k</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:range> </math> <rendering item-idref="4"/> </region> <region region-id="1423" left="12" top="162.75" width="489.75" height="165" align-x="12" align-y="174" 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 m - порядок дифференциального<sp count="2"/>уравнения; К - число дискретных точек </f> <f family="Arial Cyr" charset="204" size="12">отсчета; i - порядок производной; </f> <region region-id="1417" left="198.75" top="177.75" width="21" height="17.25" align-x="208.5" align-y="189" 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">Z</ml:id> <ml:sequence> <ml:id xml:space="preserve">i</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:sequence> </ml:apply> </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"> - дискретные значения искомого решения, записываемые в матрицу "Z"; H - кубическая матрица известных коэффициентов. </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Ниже приводится алгоритм решения для случая 3-х диагональной матрицы. Надо сказать, </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">что методы "стрельбы", "прогонки" являются частными случаями метода Гаусса. Параметры </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">дифференциального<sp count="2"/>уравнения</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>следующие: m=2,<sp count="2"/>далее см. по тексту. </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false" line-through="false">Иллюстрацию этого метода проведем на решении уравнения:</inlineAttr> </f> <region region-id="1425" left="12" top="288" width="95.25" height="15" align-x="78.75" align-y="299.25" 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:plus/> <ml:id xml:space="preserve">Z''</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:id xml:space="preserve">Z</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="6"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">,<sp count="2"/>с граничными условиями </inlineAttr> </f> <region region-id="1426" left="261.75" top="288" width="120" height="17.25" align-x="317.25" align-y="299.25" 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:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <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:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">K</ml:id> </ml:apply> </ml:apply> </ml:sequence> </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"> (здесь </inlineAttr> </f> <inlineAttr font-weight="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> Z </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">i,k</inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">,</f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="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">i=1..</f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" underline="false" line-through="false"> m </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">-1</f> </inlineAttr> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">отсутствуют - есть только </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> Z </f> <f family="Arial Cyr" charset="204" size="12"> o </f> <f family="Arial Cyr" charset="204" size="12">,k</f> <f family="Arial Cyr" charset="204" size="12">. Поэтому у </f> <f family="Arial Cyr" charset="204" size="12">Z</f> <f family="Arial Cyr" charset="204" size="12"> можно оставить один индекс, например, </f> <f family="Arial Cyr" charset="204" size="12"> k </f> <f family="Arial Cyr" charset="204" size="12">).</f> </text> </region> <region region-id="1440" left="12" top="342.75" width="210" height="13.5" align-x="12" align-y="354" 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">Перейдем к дискретным переменным:</f> </text> </region> <region region-id="1450" left="234" top="342.75" width="45" height="15.75" align-x="264" align-y="354" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:range xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">j</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:id xml:space="preserve">K</ml:id> </ml:range> </math> <rendering item-idref="8"/> </region> <region region-id="1582" left="294" top="342.75" width="34.5" height="17.25" align-x="312" align-y="354" 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:real>0</ml:real> </ml:apply> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </math> <rendering item-idref="9"/> </region> <region region-id="1583" left="348" top="342.75" width="59.25" height="17.25" align-x="363.75" align-y="354" 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">j</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">j</ml:id> <ml:id xml:space="preserve">h</ml:id> </ml:apply> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="10"/> </region> <region region-id="1584" left="432" top="342.75" width="36" height="17.25" align-x="451.5" align-y="354" 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">K</ml:id> </ml:apply> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </math> <rendering item-idref="11"/> </region> <region region-id="1456" left="18" top="379.5" width="486.75" height="142.5" align-x="18" align-y="390" 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 запишем рекуррентные формулы вычисления<sp count="2"/>решения<sp count="3"/>исходного<sp count="2"/>дифференци- ального уравнения, представленного в разностном виде: </f> <region region-id="122" left="18" top="407.25" width="189.75" height="39.75" align-x="174.75" align-y="428.25" 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:plus/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </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:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">P</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </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"> ,<sp count="3"/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">Выразим из этого уравнения : </f> <region region-id="1457" left="18" top="447.75" width="195.75" height="22.5" align-x="47.25" align-y="464.25" 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">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="13"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> .<sp count="2"/>(здесь<sp count="2"/>j=1, 2, ...). Далее найдём</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> функциональную зависимость F: </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="1586" left="107.25" top="471" width="96" height="17.25" align-x="124.5" align-y="482.25" 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">Z</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">F</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:sequence> </ml:apply> </ml:apply> </math> <rendering item-idref="14"/> </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="10"> <inlineAttr font-weight="normal" underline="false" line-through="false">Примечание</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Выразить Z</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> j </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> <f family="Arial Cyr" charset="204" size="10">как </f> <region region-id="1585" left="153" top="489" width="96" height="17.25" align-x="170.25" align-y="500.25" 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">Z</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">F</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:sequence> </ml:apply> </ml:apply> </math> <rendering item-idref="15"/> </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="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">можно в общем случае только<sp count="2"/>для линейных дифференциальных уравнений. </inlineAttr> </f> </text> </region> <region region-id="1696" left="18" top="538.5" width="238.5" height="40.5" align-x="35.25" align-y="558" 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">Z</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">j</ml:id> </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:parens> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="16"/> </region> <region region-id="1695" left="294" top="546.75" width="60" height="15.75" align-x="304.5" align-y="558" 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">j</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1..</ml:real> <ml:id xml:space="preserve">K</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="17"/> </region> <region region-id="1694" left="444" top="546.75" width="17.25" height="15.75" align-x="451.5" align-y="558" 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="1698" left="18" top="594" width="475.5" height="30.75" align-x="18" align-y="606" 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 (1) задает СЛАУ из (</f> <f family="Arial Cyr" charset="204" size="12"> К </f> <f family="Arial Cyr" charset="204" size="12">-1) уравнений и </f> <f family="Arial Cyr" charset="204" size="12">(</f> <f family="Arial Cyr" charset="204" size="12"> К </f> <f family="Arial Cyr" charset="204" size="12">-1) неизвестных, из которых надо определить (Z</f> <f family="Arial Cyr" charset="204" size="12"> 1 </f> <f family="Arial Cyr" charset="204" size="12">, ... ,Z</f> <f family="Arial Cyr" charset="204" size="12">K-1</f> <f family="Arial Cyr" charset="204" size="12">), а<sp count="2"/>Z</f> <f family="Arial Cyr" charset="204" size="12"> 0 </f> <f family="Arial Cyr" charset="204" size="12"> и Z</f> <f family="Arial Cyr" charset="204" size="12"> K </f> <f family="Arial Cyr" charset="204" size="12"> - известны из граничных условий.</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="1647" left="450" top="648.75" width="17.25" height="15.75" align-x="457.5" align-y="660" 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="19"/> </region> <region region-id="1593" left="24" top="654.75" width="119.25" height="13.5" align-x="24" align-y="666" 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">Введём обозначения:</f> </text> </region> <region region-id="1595" left="174" top="646.5" width="78.75" height="40.5" align-x="193.5" align-y="666" 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">Q</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="20"/> </region> <region region-id="1594" left="294" top="649.5" width="112.5" height="22.5" align-x="312" align-y="666" 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">φ</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">j</ml:id> </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:parens> </ml:apply> </ml:apply> </math> <rendering item-idref="21"/> </region> <region region-id="1650" left="24" top="708.75" width="81.75" height="13.5" align-x="24" 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">Тогда получим:</f> </text> </region> <region region-id="1651" left="132" top="703.5" width="163.5" height="22.5" align-x="149.25" 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:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">j</ml:id> </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:parens> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="22"/> </region> <region region-id="1653" left="456" top="708.75" width="17.25" height="15.75" align-x="463.5" 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:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>3</ml:real> </ml:parens> </math> <rendering item-idref="23"/> </region> <region region-id="1707" left="24" top="750.75" width="354" height="23.25" align-x="24" align-y="768" 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">Из (3) для j=1 следует: </f> <region region-id="1708" left="150.75" top="751.5" width="226.5" height="22.5" align-x="310.5" align-y="768" 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:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>1</ml:real> </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:parens> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="24"/> </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="1596" left="24" top="785.25" width="487.5" height="84.75" align-x="24" 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">Так как Z</f> <f family="Arial Cyr" charset="204" size="12"> o </f> <f family="Arial Cyr" charset="204" size="12"> известно из граничных условий, то, следовательно, известно и </f> <region region-id="1597" left="432" top="786" width="13.5" height="18" align-x="438" 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:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="25"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Поэтому </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(3) для j=1 можно записать как </inlineAttr> </f> <region region-id="1598" left="196.5" top="809.25" width="64.5" height="17.25" align-x="216" align-y="820.5" 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:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">F</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </math> <rendering item-idref="26"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Эта зависимость определяет предыдущее</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">значение Z через последующее пока неизвестное. Нам же надо найти всё множество значений {Z</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">j</inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">}, j=1,2,...,K-1. Поступая как в предыдущем случае, найдём зависимость F</f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> j </inlineAttr> </f> <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">для j=2, записав формулу (3): </inlineAttr> </f> </text> </region> <region region-id="1617" left="48" top="894" width="86.25" height="18" align-x="67.5" 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:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="27"/> </region> <region region-id="1616" left="150" top="894.75" width="33.75" height="13.5" align-x="150" 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">Здесь</f> </text> </region> <region region-id="1615" left="192" top="889.5" width="109.5" height="22.5" align-x="212.25" 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:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>2</ml:real> </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:parens> </ml:apply> </ml:apply> </math> <rendering item-idref="28"/> </region> <region region-id="1612" left="36" top="929.25" width="468" height="18.75" align-x="36" align-y="942" 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 в выражение для </f> <region region-id="1709" left="199.5" top="930" width="13.5" height="18" align-x="205.5" align-y="942" 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">φ</ml:id> <ml:real>2</ml:real> </ml:apply> </math> <rendering item-idref="29"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> найденное ранее </inlineAttr> </f> <region region-id="1710" left="316.5" top="930.75" width="12.75" height="17.25" align-x="321.75" align-y="942" 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">Z</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="30"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> и запишем</inlineAttr> </f> </text> </region> <region region-id="1643" left="36" top="976.5" width="345" height="40.5" align-x="55.5" align-y="996" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="true" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>1</ml:real> </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:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>2</ml:real> </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:parens> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="31"/> </region> <region region-id="1669" left="36" top="1032.75" width="464.25" height="52.5" align-x="36" align-y="1044" 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">Последнее уравнение линейно связывает Z</f> <f family="Arial Cyr" charset="204" size="12"> 2 </f> <f family="Arial Cyr" charset="204" size="12"> и Z</f> <f family="Arial Cyr" charset="204" size="12"> 3 </f> <f family="Arial Cyr" charset="204" size="12"> и позволяет выразить<sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12">Z</f> <f family="Arial Cyr" charset="204" size="12"> 2 </f> <f family="Arial Cyr" charset="204" size="12"> <sp count="3"/>через </f> <f family="Arial Cyr" charset="204" size="12">Z</f> <f family="Arial Cyr" charset="204" size="12">3</f> <f family="Arial Cyr" charset="204" size="12">, то есть получить зависимость </f> <region region-id="1620" left="222.75" top="1050.75" width="64.5" height="17.25" align-x="242.25" align-y="1062" 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">Z</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">F</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:parens> </ml:apply> </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">. Теоретически эту зависимость </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">найти </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">можно так</inlineAttr> </f> </text> </region> <region region-id="1639" left="42" top="1098.75" width="30.75" height="15" align-x="56.25" align-y="1110" 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">Given</ml:id> </math> <rendering item-idref="33"/> </region> <region region-id="1644" left="48" top="1123.5" width="258" height="22.5" align-x="67.5" align-y="1140" 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">z2</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">q2</ml:id> <ml:id xml:space="preserve">z3</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">q2</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">q1</ml:id> <ml:id xml:space="preserve">z2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">q1</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">z0</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>1</ml:real> </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:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>2</ml:real> </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:apply> </ml:apply> </math> <rendering item-idref="34"/> </region> <region region-id="1645" left="54" top="1159.5" width="379.5" height="22.5" align-x="108" align-y="1176" 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:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:id xml:space="preserve">z2</ml:id> </ml:apply> <ml:symResult> <ml:apply> <ml:id xml:space="preserve">RootOf</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">_Z</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">q2</ml:id> <ml:id xml:space="preserve">z3</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">q2</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">q1</ml:id> <ml:id xml:space="preserve">_Z</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">q1</ml:id> <ml:id xml:space="preserve">z0</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">q1</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>1</ml:real> </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:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>2</ml:real> </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:apply> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="35"/> </region> <region region-id="1699" left="36" top="1194.75" width="471" height="25.5" align-x="36" align-y="1206" 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">. Однако определение z2 через RootOf практического значения не находит. В Maple</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="10">это сделать </f> <f family="Arial Cyr" charset="204" size="10">проще, используя опцию </f> <f family="Arial Cyr" charset="204" size="10"> solve </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-style="normal">или</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <sp/> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-style="normal">subs и simplify</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-style="normal">.</inlineAttr> </f> </text> </region> <region region-id="1654" left="42" top="1236.75" width="403.5" height="16.5" align-x="42" align-y="1248" 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">Приводя подобные члены и относя Z</f> <f family="Arial Cyr" charset="204" size="12"> 2 </f> <f family="Arial Cyr" charset="204" size="12"> в левую часть уравнения, получим: </f> </text> </region> <region region-id="1661" left="396" top="1272.75" width="17.25" height="15.75" align-x="403.5" align-y="1284" 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="36"/> </region> <region region-id="1655" left="54" top="1269" width="236.25" height="36.75" align-x="73.5" 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:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>2</ml:real> </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:parens> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="37"/> </region> <region region-id="1656" left="48" top="1326.75" width="155.25" height="13.5" align-x="48" align-y="1338" 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">Вновь введём обозначения:</f> </text> </region> <region region-id="1657" left="228" top="1317" width="87" height="36.75" align-x="249.75" align-y="1338" 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">C</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="38"/> </region> <region region-id="1658" left="342" top="1317" width="151.5" height="36.75" align-x="362.25" align-y="1338" 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">φ</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>2</ml:real> </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:parens> </ml:apply> </ml:apply> </math> <rendering item-idref="39"/> </region> <region region-id="1659" left="48" top="1367.25" width="399.75" height="23.25" align-x="48" align-y="1380" 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<sp count="2"/>С</f> <f family="Arial Cyr" charset="204" size="12"> 2 </f> <f family="Arial Cyr" charset="204" size="12"> и </f> <region region-id="1660" left="100.5" top="1368" width="13.5" height="18" align-x="106.5" align-y="1380" 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">φ</ml:id> <ml:real>2</ml:real> </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"> по-прежнему известны. Перепишем (4) в следующем виде</inlineAttr> </f> </text> </region> <region region-id="1664" left="60" top="1416" width="86.25" height="18" align-x="79.5" align-y="1428" 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">Z</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="41"/> </region> <region region-id="1665" left="336" top="1416.75" width="17.25" height="15.75" align-x="343.5" align-y="1428" 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="42"/> </region> <region region-id="1673" left="24" top="1446.75" width="467.25" height="30" align-x="24" align-y="1458" 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">Продолжим этот процесс исключения переменных дальше. </f> <f family="Arial Cyr" charset="204" size="12">Изменяя j=1..K-1 и выражая всякий раз Z</f> <f family="Arial Cyr" charset="204" size="12"> j </f> <f family="Arial Cyr" charset="204" size="12">через</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>Z</f> <f family="Arial Cyr" charset="204" size="12"> j+1 </f> <f family="Arial Cyr" charset="204" size="12">, дойдем, наконец, до уравнения:</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="1676" left="114" top="1494" width="101.25" height="18" align-x="134.25" align-y="1506" 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">Z</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </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> </math> <rendering item-idref="43"/> </region> <region region-id="1677" left="354" top="1494.75" width="17.25" height="15.75" align-x="361.5" align-y="1506" 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="44"/> </region> <region region-id="1459" left="24" top="1529.25" width="479.25" height="121.5" align-x="24" align-y="1542" 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"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Здесь </inlineAttr> </f> <region region-id="1466" left="60" top="1530.75" width="15.75" height="17.25" align-x="66.75" align-y="1542" 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">C</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="45"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> и</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/> </f> <region region-id="1467" left="92.25" top="1530" width="14.25" height="18" align-x="98.25" align-y="1542" 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">φ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="46"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> -<sp count="2"/>известные<sp count="2"/>коэффициенты. </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">Подставим (6) в (n+1)-е уравнение (1)</f> <f family="Arial Cyr" charset="204" size="12">или (3). Вновь разрешая его: </f> <region region-id="1576" left="186" top="1548.75" width="217.5" height="22.5" align-x="218.25" align-y="1565.25" 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">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</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">f</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</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:parens> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="47"/> </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">или,<sp count="65"/>подставляя в последнее вместо<sp count="2"/>Z</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">выражение (6), получим</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="1575" left="24" top="1588.5" width="307.5" height="22.5" align-x="56.25" align-y="1605" 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">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <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:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</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:parens> </ml:apply> </ml:apply> </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">. Приведём подобные члены</inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">и</f> </inlineAttr> <f family="Times New Roman 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">н</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">айдем:<sp count="2"/> </inlineAttr> </f> <region region-id="1570" left="84.75" top="1611.75" width="299.25" height="22.5" align-x="198" align-y="1628.25" 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:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <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:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</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:parens> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="49"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> . Левую и правую части уравнения поделим на коэффициент при Z</inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">n+1</f> </inlineAttr> <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="1731" left="12" top="1668.75" width="450.75" height="59.25" align-x="12" align-y="1680" 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">Тогда выразим Z</f> <f family="Arial Cyr" charset="204" size="12"> n+1 </f> <f family="Arial Cyr" charset="204" size="12"> :</f> <region region-id="1571" left="12" top="1686.75" width="234" height="42" align-x="44.25" align-y="1713" 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">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <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:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</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:parens> </ml:apply> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="50"/> </region> <f family="Arial Cyr" charset="204" size="12"> , где (см.(2))<sp count="2"/> </f> <region region-id="1572" left="315.75" top="1693.5" width="105.75" height="40.5" align-x="350.25" align-y="1713" 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">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="51"/> </region> <f family="Arial Cyr" charset="204" size="12"> .</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="1732" left="12" top="1746.75" width="468" height="32.25" align-x="12" align-y="1758" 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 итоге </f> <f family="Arial Cyr" charset="204" size="12">получим:</f> <region region-id="1463" left="12" top="1761.75" width="137.25" height="18" align-x="44.25" align-y="1773.75" 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">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="52"/> </region> <f family="Arial Cyr" charset="204" size="12"> ,<sp count="2"/>где </f> <f family="Arial Cyr" charset="204" size="12"> n = 0,1, ..., (K-2).</f> </text> </region> <region region-id="1730" left="372" top="1752.75" width="17.25" height="15.75" align-x="379.5" align-y="1764" 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="53"/> </region> <region region-id="1734" left="18" top="1794.75" width="455.25" height="56.25" align-x="18" align-y="1806" 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">Коэффициенты в (7) определяются по тождественным реккурентным формулам</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="1468" left="21" top="1809.75" width="233.25" height="42" align-x="175.5" align-y="1830.75" 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:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="54"/> </region> <f family="Arial Cyr" charset="204" size="12">,<sp count="2"/> </f> <region region-id="1480" left="258.75" top="1814.25" width="149.25" height="22.5" align-x="291.75" align-y="1830.75" 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">φ</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <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:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</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:parens> </ml:apply> </ml:apply> </math> <rendering item-idref="55"/> </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"> <sp count="9"/>(8)</f> </text> </region> <region region-id="1737" left="24" top="1860" width="229.5" height="18.75" align-x="24" align-y="1872" 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">Причём следует считать, что C</f> <f family="Arial Cyr" charset="204" size="12"> 0 </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr>=0, </inlineAttr> </f> <f family="Symbol" charset="2" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">f</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> 0 </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr>=0.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr> <sp count="2"/> </inlineAttr> </f> </text> </region> <region region-id="1733" left="24" top="1896" width="471.75" height="73.5" align-x="24" 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="true"> <f family="Arial Cyr" charset="204" size="12">Исходя из (3) и общей формулы (7), которая при </f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">=0 должна сводиться к (3), при </f> <f family="Arial Cyr" charset="204" size="12">изме</f> <f family="Arial Cyr" charset="204" size="12">нении индекса </f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">=0,1,... следует положить </f> <region region-id="1713" left="283.5" top="1911.75" width="45.75" height="17.25" align-x="305.25" align-y="1923" 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">C</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="56"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, если </inlineAttr> </f> <region region-id="1714" left="364.5" top="1911.75" width="37.5" height="17.25" align-x="386.25" align-y="1923" 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">C</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="57"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. А</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> из равен-</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">ства </inlineAttr> </f> <region region-id="1715" left="51" top="1932.75" width="110.25" height="22.5" align-x="71.25" align-y="1949.25" 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">φ</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:real>1</ml:real> </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:parens> </ml:apply> </ml:apply> </math> <rendering item-idref="58"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> следует </inlineAttr> </f> <region region-id="1716" left="209.25" top="1937.25" width="42" height="18" align-x="229.5" align-y="1949.25" 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">φ</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="59"/> </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">Здесь </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="1688" left="296.25" top="1929.75" width="108.75" height="40.5" align-x="330.75" align-y="1949.25" 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">Q</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </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"> (см. (2))</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="1552" left="24" top="1980.75" width="491.25" height="116.25" align-x="24" align-y="1992" 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, коэффициенты уравнений (7), связывающих последующие и преды-</f> <f family="Arial Cyr" charset="204" size="12">дущие значения </f> <f family="Arial Cyr" charset="204" size="12"> (Z</f> <f family="Arial Cyr" charset="204" size="12"> n<sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12">и</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="3"/> </f> <f family="Arial Cyr" charset="204" size="12">Z</f> <f family="Arial Cyr" charset="204" size="12"> n+1 </f> <f family="Arial Cyr" charset="204" size="12">)</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">, можно определять из рекуррентных соотношений (8) </f> <f family="Arial Cyr" charset="204" size="12">при начальных значен</f> <f family="Arial Cyr" charset="204" size="12">иях для: </f> <region region-id="1483" left="197.25" top="2013" width="37.5" height="17.25" align-x="219" align-y="2024.25" 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">C</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>0</ml:real> </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"> <sp/> </inlineAttr> </f> <region region-id="1484" left="237.75" top="2012.25" width="42" height="18" align-x="258" align-y="2024.25" 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">φ</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="62"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Так<sp count="2"/>как<sp count="2"/>Z</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">K<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">известно, то после нахож-</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">де</inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">ния всех коэффициентов C</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"> , </inlineAttr> </f> <region region-id="1485" left="204" top="2035.5" width="14.25" height="18" align-x="210" align-y="2047.5" 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:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="63"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> можно последовательно определять<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/> </inlineAttr> </f> <region region-id="1486" left="27" top="2059.5" width="63.75" height="17.25" align-x="74.25" align-y="2070.75" 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:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">K</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:real>....</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:sequence> </math> <rendering item-idref="64"/> </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">из (6). Процесс вычисления коэффициентов </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12">C</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12"> , </f> <region region-id="1516" left="367.5" top="2058.75" width="14.25" height="18" align-x="373.5" align-y="2070.75" 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">φ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="65"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> принято называть </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr underline="false" line-through="false">прямым<sp count="2"/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr underline="false" line-through="false"> ходом </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> прогонки, а п</f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12">роцесс вычисления </f> <f family="Arial Cyr" charset="204" size="12">Z</f> <f family="Arial Cyr" charset="204" size="12"> n<sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12">- </f> <f family="Arial Cyr" charset="204" size="12">обратным ходом </f> <f family="Arial Cyr" charset="204" size="12">прогонки.</f> </text> </region> <region region-id="1738" left="24" top="2130.75" width="485.25" height="51" align-x="24" align-y="2148" 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">Пример. Рассмотрим на примере решения уравнения </f> <region region-id="49" left="329.25" top="2131.5" width="91.5" height="20.25" align-x="391.5" align-y="2148" 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:id xml:space="preserve">y''</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:id xml:space="preserve">y</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="66"/> </region> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>с граничными </f> <f family="Arial Cyr" charset="204" size="12">условиями: </f> <region region-id="1553" left="90" top="2152.5" width="45.75" height="15.75" align-x="120" align-y="2163.75" 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:id xml:space="preserve">y</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>1</ml:real> </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">,<sp count="2"/> </inlineAttr> </f> <region region-id="1554" left="145.5" top="2152.5" width="45.75" height="15.75" align-x="175.5" align-y="2163.75" 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:id xml:space="preserve">y</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:real>2</ml:real> </ml:apply> </math> <rendering item-idref="68"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>работу этого метода </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">(следует заметить, что не для любых краевых условий подобные задачи имеют решение).</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="1556" left="24" top="2202.75" width="478.5" height="13.5" align-x="36.75" align-y="2214" 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"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Точное решение этого уравнения, полученное ранее,<sp count="2"/>при p(x)=1 </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">есть</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="1431" left="36" top="2230.5" width="306" height="33.75" align-x="66.75" align-y="2250" 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="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.xmcd" 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<ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:real>-4</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="69"> <element-image-map> <box left="1.5" top="0.75" width="304.5" height="32.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1432" left="360" top="2238.75" width="56.25" height="15.75" align-x="393" align-y="2250" 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:provenance expr-id="1"> <originRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> 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xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1433" left="438" top="2238.75" width="56.25" height="15.75" align-x="471" align-y="2250" 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:provenance expr-id="1"> <originRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.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">9e46a6caabef99fad916a5d4b9059406</contentHash> <ml:apply> <ml:id xml:space="preserve">yt</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:provenance> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>2</ml:real> </result> </ml:eval> </math> <rendering item-idref="71"> <element-image-map> <box left="1.5" top="0.75" width="24.75" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1528" left="18" top="2292.75" width="127.5" height="13.5" align-x="18" align-y="2304" 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">Введем обозначения:</f> </text> </region> <region region-id="1739" left="162" top="2287.5" width="57.75" height="20.25" align-x="189.75" align-y="2304" 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="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.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">51727d0ea280e42932ac19c84d9aef9c</contentHash> <ml:define> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="72"> <element-image-map> <box left="1.5" top="0.75" width="56.25" height="18.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1527" left="18" top="2322" width="93.75" height="16.5" align-x="18" align-y="2334" 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">Дано:</f> <region region-id="1424" left="49.5" top="2322.75" width="48.75" height="15.75" align-x="81.75" align-y="2334" 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">P</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="73"/> </region> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="1557" left="114" top="2322.75" width="89.25" height="15.75" align-x="131.25" align-y="2334" 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:real>5</ml:real> <ml:id xml:space="preserve">FRAME</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="74"/> </region> <region region-id="1536" left="216" top="2322.75" width="47.25" height="15.75" align-x="228" align-y="2334" 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="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.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">0b580a5f0cd970190c98a1f010237f7b</contentHash> <ml:define> <ml:id xml:space="preserve">j</ml:id> <ml:range> <ml:real>0</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:range> </ml:define> </ml:provenance> </math> <rendering item-idref="75"> <element-image-map> <box left="1.5" top="0.75" width="45.75" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1537" left="282" top="2322.75" width="32.25" height="15.75" align-x="297.75" align-y="2334" 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="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.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">a965492222e0660fecda95685c52e14b</contentHash> <ml:define> <ml:id xml:space="preserve">a</ml:id> <ml:real>0</ml:real> </ml:define> </ml:provenance> </math> <rendering item-idref="76"> <element-image-map> <box left="1.5" top="0.75" width="30.75" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1538" left="324" top="2322.75" width="32.25" height="15.75" align-x="339.75" align-y="2334" 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="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.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">8478bff1e34ef83244d30da3d4617af0</contentHash> <ml:define> <ml:id xml:space="preserve">b</ml:id> <ml:real>4</ml:real> </ml:define> </ml:provenance> </math> <rendering item-idref="77"> <element-image-map> <box left="1.5" top="0.75" width="30.75" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1539" left="366" top="2315.25" width="55.5" height="32.25" align-x="381" align-y="2334" 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="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.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">895772ad97b5f283362e8ce2822c1c63</contentHash> <ml:define> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="78"> <element-image-map> <box left="1.5" top="0.75" width="54" height="30.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1540" left="438" top="2322.75" width="45.75" height="15.75" align-x="451.5" align-y="2334" 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:provenance expr-id="1"> <originRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.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">e7bc9de7c6f0c5330ae91971ef8d3b69</contentHash> <ml:id xml:space="preserve">h</ml:id> </ml:provenance> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.8</ml:real> </result> </ml:eval> </math> <rendering item-idref="79"> <element-image-map> <box left="1.5" top="0.75" width="5.25" height="13.5" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="67" left="12" top="2358.75" width="210" height="13.5" align-x="12" align-y="2370" 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">Перейдем к дискретным переменным:</f> </text> </region> <region region-id="1702" left="240" top="2358.75" width="36.75" height="17.25" align-x="259.5" align-y="2370" 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="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="e6852821-e88b-406e-8fc5-1b2977286bf4" version-id="094fd3f1-7f8a-4974-907a-bbe1afc4ba0f" branch-id="00000000-0000-0000-0000-000000000000" revision-num="9" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЧислМетоды\КраевыеЗадачи\МетСтрельбы1.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">b45f53bc7cc59dfe49f4486d93bc6b58</contentHash> <ml:define> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:id xml:space="preserve">a</ml:id> </ml:define> </ml:provenance> </math> <rendering item-idref="80"> <element-image-map> <box left="1.5" top="0.75" width="35.25" height="15.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1703" left="312" top="2358.75" width="65.25" height="17.25" align-x="329.25" align-y="2370" 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">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">j</ml:id> <ml:id xml:space="preserve">h</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="81"/> </region> <region region-id="1704" left="396" top="2358.75" width="42.75" height="17.25" align-x="415.5" align-y="2370" 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">x</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>4</ml:real> </result> </ml:eval> </math> <rendering item-idref="82"/> </region> <region region-id="71" left="12" top="2394.75" width="109.5" height="13.5" align-x="12" align-y="2406" 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="72" left="138" top="2394.75" width="38.25" height="17.25" align-x="159.75" 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:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Y</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="83"/> </region> <region region-id="73" left="198" top="2394.75" width="39.75" height="17.25" align-x="221.25" 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:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:define> </math> <rendering item-idref="84"/> </region> <region region-id="1499" left="264" top="2394.75" width="39.75" height="17.25" align-x="287.25" 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:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="85"/> </region> <region region-id="1500" left="330" top="2394" width="45" height="18" align-x="351.75" 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:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:real>0</ml:real> </ml:apply> <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="86"/> </region> <region region-id="74" left="12" top="2424" width="491.25" height="49.5" align-x="12" align-y="2436" 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 введены обозначения: </f> <region region-id="97" left="222.75" top="2424.75" width="11.25" height="17.25" align-x="227.25" align-y="2436" 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">Y</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </math> <rendering item-idref="87"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> - дискретные значения<sp count="2"/>решения<sp count="2"/>дифференциального<sp count="2"/>уравнения;<sp count="2"/> </inlineAttr> </f> <region region-id="98" left="204" top="2442.75" width="18" height="17.25" align-x="212.25" align-y="2454" 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">Y1</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </math> <rendering item-idref="88"/> </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">дискретные значения 1-й производной<sp count="2"/>решения<sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12">дифференциального </f> <f family="Arial Cyr" charset="204" size="12"> уравнения. </f> <f family="Arial Cyr" charset="204" size="12">Согласно формулам (7) и (8) будем иметь:</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="1487" left="36" top="2496.75" width="58.5" height="17.25" align-x="56.25" align-y="2508" 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="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">P</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="89"/> </region> <region region-id="1488" left="120" top="2496.75" width="49.5" height="17.25" align-x="135.75" align-y="2508" 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="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:id 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width="189.75" height="81.75" align-x="48" align-y="2544" 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">C</ml:id> <ml:program> <ml:for> <ml:id xml:space="preserve">j</ml:id> <ml:range> <ml:real>0</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:range> <ml:localDefine> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:real>2</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">P</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:localDefine> </ml:for> <ml:id xml:space="preserve">C</ml:id> </ml:program> </ml:define> </math> <rendering item-idref="94"/> </region> <region region-id="1506" left="288" top="2538" width="197.25" height="66" align-x="304.5" align-y="2550" 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">φ</ml:id> <ml:program> <ml:for> <ml:id xml:space="preserve">j</ml:id> <ml:range> <ml:real>0</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:range> <ml:localDefine> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</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:parens> </ml:apply> </ml:localDefine> </ml:for> <ml:id xml:space="preserve">φ</ml:id> </ml:program> </ml:define> </math> <rendering item-idref="95"/> </region> <region region-id="1740" left="24" top="2648.25" width="474" height="72" align-x="24" align-y="2658" 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">. Проверка этих алгоритмов сделана в Maple: файл "МетПрогонки_приложение.mws"</f> <f family="Arial Cyr" charset="204" size="12">После нахождения всех коэффициентов C</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12"> , </f> <region region-id="1517" left="276" top="2661" width="14.25" height="18" align-x="282" align-y="2673" 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">φ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="96"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, записанных в векторы C и </inlineAttr> </f> <f family="Symbol" charset="2" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">f</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> можно последовательно определять<sp count="3"/> </f> <region region-id="1518" left="197.25" top="2684.25" width="65.25" height="17.25" align-x="245.25" align-y="2695.5" 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:indexer/> <ml:id xml:space="preserve">Y</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:real>....</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Y</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:sequence> </math> <rendering item-idref="97"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">,<sp count="2"/>таким образом:</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="1558" left="362.25" top="2684.25" width="66.75" height="15.75" align-x="374.25" align-y="2695.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i</ml:id> <ml:range> <ml:real>0</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="98"/> </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"> <sp count="3"/> </inlineAttr> </f> <region region-id="1559" left="24" top="2702.25" width="168" height="18" align-x="68.25" 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:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Y</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">i</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">i</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Y</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">i</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="99"/> </region> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="1742" left="48" top="2832" width="361.5" height="223.5" align-x="48" align-y="2832" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="100"/> <rendering item-idref="101"/> </region> <region region-id="1744" left="438" top="2910.75" width="45.75" height="15.75" align-x="451.5" align-y="2922" 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">h</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.8</ml:real> </result> </ml:eval> </math> <rendering item-idref="102"/> </region> <region region-id="1746" left="444" top="2946.75" width="43.5" height="17.25" align-x="464.25" align-y="2958" 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:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="103"/> </region> <region region-id="1747" left="444" top="2976.75" width="45" height="17.25" align-x="465.75" align-y="2988" 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">N</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>2</ml:real> </result> </ml:eval> </math> <rendering item-idref="104"/> </region> <region region-id="1748" left="42" top="3114.75" width="441" height="13.5" align-x="42" align-y="3126" 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">Рис. 1. </f> <f family="Arial Cyr" charset="204" size="12">Возможна анимация </f> <f family="Arial Cyr" charset="204" size="12">графика.(50 кадров).</f> </text> </region> <region region-id="1706" left="42" top="3150.75" width="221.25" height="13.5" align-x="42" align-y="3162" 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">Точность решения зависит только от "h".</f> </text> </region> <region region-id="1545" left="30" top="3186" width="478.5" height="59.25" align-x="30" 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"> Упражнение . </f> <f family="Arial Cyr" charset="204" size="12">Решить численно </f> <f family="Arial Cyr" charset="204" size="12"> дифференциальное уравнение </f> <region region-id="1724" left="384.75" top="3186.75" width="95.25" height="15" align-x="451.5" align-y="3198" 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:id xml:space="preserve">Z''</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:id xml:space="preserve">Z</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="105"/> </region> <f family="Arial Cyr" charset="204" size="12">для </f> <f family="Arial Cyr" charset="204" size="12">различных p(x):<sp count="2"/>x</f> <f family="Arial Cyr" charset="204" size="12"> 2 </f> <f family="Arial Cyr" charset="204" size="12">,<sp count="2"/>x</f> <f family="Arial Cyr" charset="204" size="12"> 3 </f> <f family="Arial Cyr" charset="204" size="12">,<sp count="2"/>sin(x)<sp count="2"/>и др.<sp count="3"/>и<sp count="2"/>f(x): sin(x),<sp count="2"/>cos(x)<sp count="2"/>и др.</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">Запишем краевые условия: y(0)=1,<sp count="2"/>y(4)=2. Найдём y(1)=_____ и сравним это </f> <f family="Arial Cyr" charset="204" size="12">значение </f> <f family="Arial Cyr" charset="204" size="12">с тем, которое получим в Maple (Пример №1) R(1)=______ .</f> </text> </region> </regions> <binaryContent> <item item-id="1" content-encoding="gzip">H4sIAAAAAAAA/4yNvQ6CQBCEdzlQwd/GGhMbj9InsCBWJj6CnvifEA1SWPrm5+yCvUf2GGa/ GQZExBiHSVQb3OPjcnep3PO6Oz+q0tURyZljYrVzVzu1aIHplcX2cD8VdWPtmxcFM1ym7Z9K q2r5Stz79lprtVE2w2y4ZZvj8RBn/7u/8m5dueK0zANd2RZMeUJs2Ytitlj6lAO2BtGUDdvQ ixOCIQ8RgfmssOoII6muMhA9YQSOpUfiCRiN98FofABG40P9F8RIGYixMAJ/AQAA//8DAMuS Xhh8AQAA</item> <item item-id="2">iVBORw0KGgoAAAANSUhEUgAAAQIAAABBCAYAAAA69KomAAAAAXNSR0IArs4c6QAAAARnQU1B AACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAaCSURBVHhe7Z0LkqMgEIZzrhzI83ia XCaHydCAifJo3oy2/1dFbbmbUQLdH41mso8PAOD2QAQAAIgAAAARAAAUEAFI814/z8fzs77t MRAHRAB4Xsvn8XioBhFIBiKQxLZyr1vyqra8dslsj4t5fRaIQDQQgSS0CHbJvglgO64u8SEC 6UAEkrAi+C36lMDccS4QgXQgAkl4K76bwBABCAMRSKJABK/F3jMINc8UEIF0IAJJoCIAlUAE 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