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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="1046" 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="1" left="42" top="23.25" width="432.75" height="197.25" align-x="42" align-y="36" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="14">1.2 Метод Адамса.</f> <f family="Arial Cyr" charset="204" size="12">Решить уравнение вида: </f> <region region-id="237" left="177.75" top="39.75" width="80.25" height="36.75" align-x="214.5" align-y="60.75" 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:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:sequence> </ml:apply> </ml:apply> </math> <rendering item-idref="2"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> для заданных начальных</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> условий </inlineAttr> </f> <region region-id="238" left="90.75" top="77.25" width="9" height="17.25" align-x="94.5" align-y="88.5" 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">t</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="3"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, </inlineAttr> </f> <region region-id="239" left="106.5" top="77.25" width="52.5" height="17.25" align-x="138.75" align-y="88.5" 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:id xml:space="preserve">x</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="4"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">,<sp count="2"/>численно методом конечных разностей. </f> </inlineAttr> <region region-id="194" left="387" top="77.25" width="51.75" height="17.25" align-x="422.25" align-y="88.5" 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:lessOrEqual/> <ml:apply> <ml:lessOrEqual/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </math> <rendering item-idref="5"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">Запишем формулу Адамса с четырьмя членами [2]: </f> </inlineAttr> <region region-id="189" left="42" top="108.75" width="235.5" height="33.75" align-x="75" align-y="128.25" 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">X</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">h</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:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ΔX'</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>5</ml:real> <ml:id xml:space="preserve">h</ml:id> </ml:apply> <ml:real>12</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">Δ</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X'</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="6"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">,<sp count="44"/>(6)</f> </inlineAttr> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">где </f> </inlineAttr> <region region-id="190" left="62.25" top="149.25" width="75.75" height="17.25" align-x="75.75" align-y="160.5" 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"> 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<ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X'</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X'</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="8"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, </inlineAttr> </f> <region region-id="192" left="261" top="143.25" width="146.25" height="23.25" align-x="313.5" align-y="160.5" 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:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">Δ</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X'</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ΔX'</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ΔX'</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="9"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, </inlineAttr> </f> <region region-id="193" left="42" top="167.25" width="126.75" height="17.25" align-x="102" align-y="178.5" 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xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:sequence> </math> <rendering item-idref="11"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">,<sp count="2"/>определить </f> </inlineAttr> <region region-id="196" left="425.25" top="185.25" width="26.25" height="17.25" align-x="437.25" align-y="196.5" 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">X</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="12"/> </region> <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" font-style="normal" underline="false" line-through="false">Таким образом, зная </inlineAttr> </f> <region region-id="197" left="158.25" top="203.25" width="53.25" height="17.25" align-x="193.5" align-y="214.5" 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">X</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:real font="0">1</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:real font="0">2</ml:real> </ml:apply> </ml:sequence> </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"/>мы можем определить </inlineAttr> </f> <region region-id="198" left="348" top="203.25" width="14.25" height="17.25" align-x="354" align-y="214.5" 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">X</ml:id> <ml:real>3</ml:real> </ml:apply> </math> <rendering item-idref="14"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> и далее </f> </inlineAttr> <region region-id="199" left="411" top="203.25" width="46.5" height="17.25" align-x="426.75" align-y="214.5" 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">X</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:sequence> <ml:real>5</ml:real> <ml:id xml:space="preserve" font="1">...</ml:id> </ml:sequence> </ml:apply> </ml:sequence> </math> <rendering item-idref="15"/> </region> </text> </region> <region region-id="240" left="42" top="228" width="430.5" height="27.75" align-x="42" align-y="240" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Моделирование алгоритма Адамса в системе MathCAD. </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false">(</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false">На примере задачи, решенной выше.)</inlineAttr> </f> </text> </region> <region region-id="967" left="0" top="273" width="6008.25" align-x="8.25" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="" height="170.25"> <area is-collapsed="false" name="" show-name="false" show-border="true" show-icon="true" show-timestamp="true" allow-expand="false" is-locked="false" timestamp="" top-lock-id="967" bottom-lock-id="968" bottom-tag=""> <region region-id="977" left="24" top="282.75" width="173.25" height="13.5" align-x="24" align-y="294" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Данные из п.1.2. 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xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">0004bb8380aa530fa95312e3e435aa17</contentHash> <ml:define> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">k</ml:id> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="34"> <element-image-map> <box left="1.5" top="0.75" width="64.5" height="15.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="250" left="42" top="600.75" width="174" height="13.5" align-x="42" align-y="612" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Просмотр численного значения:</f> </text> </region> <region region-id="251" left="228" top="600.75" width="39" height="15.75" align-x="244.5" align-y="612" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">1defac042ab898da88f3a9b49edbd193</contentHash> <ml:id xml:space="preserve">K</ml:id> </ml:provenance> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>6</ml:real> </result> </ml:eval> </math> <rendering item-idref="35"> <element-image-map> <box left="1.5" top="0.75" width="8.25" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="252" left="288" top="600.75" width="36.75" height="15.75" align-x="302.25" align-y="612" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">c95ed2ec632c49216273a3314466dd3f</contentHash> <ml:id xml:space="preserve">b</ml:id> </ml:provenance> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>3</ml:real> </result> </ml:eval> </math> <rendering item-idref="36"> <element-image-map> <box left="1.5" top="0.75" width="6" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="253" left="42" top="633" width="450" height="72" align-x="42" align-y="660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Вычисляем значение n-й производной: </f> <region region-id="930" left="255" top="633.75" width="114.75" height="44.25" align-x="303.75" 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:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">Xn</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> </ml:lambda> <ml:degree> <ml:id xml:space="preserve">n</ml:id> </ml:degree> </ml:apply> </ml:apply> </math> <rendering item-idref="37"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> . В системе Maple достаточно предыдущей символьной записи, а в MathCAD - каждую производную надо записывать отдельно:</inlineAttr> </f> </text> </region> <region region-id="254" left="36" top="726.75" width="189.75" height="13.5" align-x="36" align-y="738" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Первая производная уже имеется:</f> </text> </region> <region region-id="255" left="252" top="726" width="97.5" height="16.5" align-x="302.25" align-y="738" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">6b81d1540e84271b9091464db770b08f</contentHash> <ml:define> <ml:function> <ml:id xml:space="preserve">X1</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="38"> <element-image-map> <box left="1.5" top="0.75" width="96" height="15" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="256" left="36" top="780.75" width="123" height="13.5" align-x="36" align-y="792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Вторая производная:<sp count="2"/> </f> </text> </region> <region region-id="257" left="174" top="771" width="229.5" height="36.75" align-x="224.25" align-y="792" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">714dad412eaa74f0e529190bf0ee15e6</contentHash> <ml:define> <ml:function> <ml:id xml:space="preserve">X2</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> <ml:parens> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="39"> <element-image-map> <box left="1.5" top="0.75" width="228" height="35.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="258" left="36" top="816.75" width="121.5" height="13.5" align-x="36" align-y="828" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Третья производная:<sp count="2"/> </f> </text> </region> <region region-id="259" left="42" top="873.75" width="378.75" height="87" align-x="92.25" align-y="900" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">5e3f48440492f58e11a15949ccd7c8cf</contentHash> <ml:define> <ml:function> <ml:id xml:space="preserve">X3</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:parens> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:plus/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:parens> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:define> </ml:provenance> </math> <rendering item-idref="40"> <element-image-map> <box left="1.5" top="0.75" width="377.25" height="85.5" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="260" left="30" top="990.75" width="452.25" height="54" align-x="30" align-y="1002" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Запись последующих производных в MathCAD становится обременительной. В </f> <f family="Arial Cyr" charset="204" size="12">Maple эту процедуру символьного дифференцирования выполняет сама система, </f> <f family="Arial Cyr" charset="204" size="12">что позволяет записывать производные практически любого порядка и вести </f> <f family="Arial Cyr" charset="204" size="12">далее с ними работу.</f> </text> </region> <region region-id="261" left="30" top="1056.75" width="454.5" height="27" align-x="30" align-y="1068" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Можно осуществить проверку<sp count="2"/>правильности </f> <f family="Arial Cyr" charset="204" size="12">вычислен</f> <f family="Arial Cyr" charset="204" size="12">ия производных для выбранных значений функции в отдельных точках:</f> </text> </region> <region region-id="262" left="30" top="1092.75" width="83.25" height="17.25" 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методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">0782eafad0908d9ca3c425e48fbe9527</contentHash> <ml:apply> <ml:id xml:space="preserve">X3</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:sequence> </ml:apply> </ml:provenance> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.9999999999997282</ml:real> </result> </ml:eval> </math> <rendering item-idref="41"> <element-image-map> <box left="1.5" top="0.75" width="52.5" height="15.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="263" left="114" top="1092.75" width="83.25" height="17.25" align-x="174.75" align-y="1104" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">399b8e58e1764d694a9e7c3389f6d971</contentHash> <ml:apply> <ml:id xml:space="preserve">X2</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:sequence> </ml:apply> </ml:provenance> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>2.0000000000000089</ml:real> </result> </ml:eval> </math> <rendering item-idref="42"> <element-image-map> <box left="1.5" top="0.75" width="52.5" height="15.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="264" left="30" top="1116.75" width="352.5" height="13.5" align-x="30" align-y="1128" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Вывод: вычисляет правильно, в том числе и для других функций.</f> </text> </region> <region region-id="265" left="30" top="1146.75" width="122.25" height="13.5" align-x="30" align-y="1158" show-border="false" show-highlight="false" is-protected="true" z-order="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> <f family="Arial Cyr" charset="204" size="12">:</f> </text> </region> <region region-id="266" left="162" top="1146" width="87.75" height="18" 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branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">9655bae07b137bb9d911a5ed58110cff</contentHash> <ml:define warning="WarnRedefinedUDFunction"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X3</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">X3</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:sequence> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="45"> <element-image-map> <box left="1.5" top="0.75" width="90.75" height="15.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="269" left="30" top="1182" width="307.5" height="14.25" align-x="30" align-y="1194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Просмотр численных значений и проверка: </f> </text> </region> <region region-id="270" left="30" top="1206.75" width="49.5" height="17.25" align-x="57" align-y="1218" 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 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xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.9999999999997282</ml:real> </result> </ml:eval> </math> <rendering item-idref="48"> <element-image-map> <box left="1.5" top="0.75" width="18.75" height="15.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="273" left="30" top="1230" width="174" height="14.25" align-x="30" align-y="1242" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Проверка завершена успешно. </f> </text> </region> <region region-id="274" left="30" top="1254" width="462" height="36" align-x="30" align-y="1266" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Используя разложение </f> <region region-id="281" left="158.25" top="1254.75" width="21.75" height="15.75" align-x="166.5" align-y="1266" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">t</ml:id> </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"> в ряд Тейлора в окрестности точки </inlineAttr> </f> <region region-id="282" left="376.5" top="1254.75" width="9" height="17.25" align-x="380.25" align-y="1266" show-border="false" show-highlight="false" is-protected="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">t</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="50"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> и беря его первые</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">четыре члена, определим таким образом </inlineAttr> </f> <region region-id="283" left="257.25" top="1272.75" width="58.5" height="17.25" align-x="278.25" 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:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="51"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="3"/>и<sp count="2"/> </inlineAttr> </f> <region region-id="284" left="337.5" top="1272.75" width="58.5" height="17.25" align-x="358.5" 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:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="52"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> как </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="285" left="36" top="1295.25" width="191.25" height="39" align-x="58.5" align-y="1320" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные 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xml:space="preserve">X1</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X2</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:parens> <ml:real>3</ml:real> </ml:apply> <ml:real>6</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X3</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="54"> <element-image-map> <box left="1.5" top="0.75" width="237" height="37.5" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="287" left="30" top="1344.75" width="454.5" height="50.25" align-x="30" align-y="1356" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Значения X</f> <f family="Arial Cyr" charset="204" size="12"> o </f> <f family="Arial Cyr" charset="204" size="12">, X</f> <f family="Arial Cyr" charset="204" size="12"> 1 </f> <f family="Arial Cyr" charset="204" size="12">, X</f> <f family="Arial Cyr" charset="204" size="12"> 2 </f> <f family="Arial Cyr" charset="204" size="12"> необходимы только вначале для запуска алгоритма Адамса.</f> <f family="Arial Cyr" charset="204" size="12">Вычисления последующих X</f> <f family="Arial Cyr" charset="204" size="12">k</f> <f family="Arial Cyr" charset="204" size="12">,<sp count="2"/> </f> <region region-id="888" left="196.5" top="1362" width="30" height="15.75" align-x="210.75" align-y="1373.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">k</ml:id> <ml:real>3</ml:real> </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"> идет автоматически по рекуррентной формуле</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">через разности.</inlineAttr> </f> </text> </region> <region region-id="889" left="36" top="1410" width="176.25" height="14.25" 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<element-image-map> <box left="1.5" top="0.75" width="48" height="16.5" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="893" left="300" top="1440" width="99.75" height="18" align-x="356.25" align-y="1452" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" 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</ml:eval> </math> <rendering item-idref="59"> <element-image-map> <box left="1.5" top="0.75" width="48" height="16.5" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="894" left="36" top="1464.75" width="99" height="13.5" align-x="36" align-y="1476" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Первые разности:</f> </text> </region> <region region-id="895" left="36" top="1494.75" width="48" height="15.75" align-x="51.75" 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:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="95589038-740e-4125-9372-18f2106d566d" 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href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">5f567507797001ea67e8556f569edc06</contentHash> <ml:define> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ΔX1</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:sequence> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="61"> <element-image-map> <box left="1.5" top="0.75" width="192" height="16.5" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="897" left="306" top="1494" width="48" height="56.25" align-x="324.75" 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:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:provenance expr-id="1"> <originRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">cb216aa32e4704db2f058b281d3366e8</contentHash> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ΔX1</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:provenance> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:matrix rows="2" cols="1"> <ml:real>1.2916666666666621</ml:real> <ml:real>2.041666666666631</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="62"/> </resultFormat> </math> <rendering item-idref="63"> <element-image-map> <box left="1.5" top="0.75" width="38.25" height="16.5" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="898" left="42" top="1560.75" width="97.5" height="13.5" align-x="42" align-y="1572" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Вторые разности:</f> </text> </region> <region region-id="899" left="42" top="1590.75" width="32.25" height="15.75" align-x="57.75" align-y="1602" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">6e7930162eb60aff26c89fc0bc6cc19b</contentHash> <ml:define> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:define> </ml:provenance> </math> <rendering item-idref="64"> <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="900" left="108" top="1590" width="150" height="18" align-x="156" align-y="1602" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">b07fc13d151e98825056130b045308cd</contentHash> <ml:define> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Δ2X</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ΔX1</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ΔX1</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="65"> <element-image-map> <box left="1.5" top="0.75" width="148.5" height="16.5" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="901" left="276" top="1590" width="84" height="18" align-x="322.5" align-y="1602" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">76594b4b732f0b44eef233cc689e6c15</contentHash> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Δ2X</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:provenance> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.74999999999996891</ml:real> </result> </ml:eval> </math> <rendering item-idref="66"> <element-image-map> <box left="1.5" top="0.75" width="38.25" height="16.5" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="902" left="36" top="1620" width="174" height="14.25" align-x="36" align-y="1632" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Проверка завершена успешно. </f> </text> </region> <region region-id="903" left="36" top="1650.75" width="418.5" height="27" align-x="36" align-y="1662" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Далее все последующие значения "х" будем вычислять по формуле Адамса,</f> <f family="Arial Cyr" charset="204" size="12">имеющей вид:</f> </text> </region> <region region-id="904" left="42" top="1698.75" width="51" height="15.75" align-x="57.75" align-y="1710" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" 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<inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">) </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">Решить уравнение x'=cos(x) при условии х(0)=0 методом Адамса.</f> <f family="Arial Cyr" charset="204" size="12">Полученные решения сравнить с точными решениями, полученными, например, с по-</f> <f family="Arial Cyr" charset="204" size="12">мощью опции Bulstoer, или dsolve, или Mathematica. </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="1024" left="36" top="2502.75" width="415.5" height="27" align-x="36" align-y="2514" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">У студентов трудности вызывает 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font-weight="normal" font-style="normal" underline="false" line-through="false"> для заданных начальных</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> условий </inlineAttr> </f> <region region-id="238" left="90.75" top="77.25" width="9" height="17.25" align-x="94.5" align-y="88.5" 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">t</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="3"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, </inlineAttr> </f> <region region-id="239" left="106.5" top="77.25" width="52.5" height="17.25" align-x="138.75" align-y="88.5" 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:id xml:space="preserve">x</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="4"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">,<sp count="2"/>численно методом конечных разностей. </f> </inlineAttr> <region region-id="194" left="387" top="77.25" width="51.75" height="17.25" align-x="422.25" align-y="88.5" 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:lessOrEqual/> <ml:apply> <ml:lessOrEqual/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </math> <rendering item-idref="5"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">Запишем формулу Адамса с четырьмя членами [2]: </f> </inlineAttr> <region region-id="189" left="42" top="108.75" width="235.5" height="33.75" align-x="75" align-y="128.25" 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">X</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">h</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:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ΔX'</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>5</ml:real> <ml:id xml:space="preserve">h</ml:id> </ml:apply> <ml:real>12</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">Δ</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X'</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="6"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">,<sp count="44"/>(6)</f> </inlineAttr> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">где </f> </inlineAttr> <region region-id="190" left="62.25" top="149.25" width="75.75" height="17.25" align-x="75.75" align-y="160.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="7"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">, </f> </inlineAttr> <region region-id="191" left="144.75" top="148.5" width="109.5" height="18" align-x="187.5" align-y="160.5" 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">ΔX'</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X'</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X'</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="8"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, </inlineAttr> </f> <region region-id="192" left="261" top="143.25" width="146.25" height="23.25" align-x="313.5" align-y="160.5" 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:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">Δ</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X'</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ΔX'</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ΔX'</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="9"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, </inlineAttr> </f> <region region-id="193" left="42" top="167.25" width="126.75" height="17.25" align-x="102" align-y="178.5" 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:equal/> <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:id xml:space="preserve">X</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <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:apply> <ml:id xml:space="preserve">X'</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:sequence> </math> <rendering item-idref="10"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">Формула Адамса дает возможность, зная </f> </inlineAttr> <region region-id="195" left="272.25" top="185.25" width="77.25" height="17.25" align-x="319.5" align-y="196.5" 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">X</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:sequence> </math> <rendering item-idref="11"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">,<sp count="2"/>определить </f> </inlineAttr> <region region-id="196" left="425.25" top="185.25" width="26.25" height="17.25" align-x="437.25" align-y="196.5" 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">X</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="12"/> </region> <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" font-style="normal" underline="false" line-through="false">Таким образом, зная </inlineAttr> </f> <region region-id="197" left="158.25" top="203.25" width="53.25" height="17.25" align-x="193.5" align-y="214.5" 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">X</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:real font="0">1</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:real font="0">2</ml:real> </ml:apply> </ml:sequence> </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"/>мы можем определить </inlineAttr> </f> <region region-id="198" left="348" top="203.25" width="14.25" height="17.25" align-x="354" align-y="214.5" 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">X</ml:id> <ml:real>3</ml:real> </ml:apply> </math> <rendering item-idref="14"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> и далее </f> </inlineAttr> <region region-id="199" left="411" top="203.25" width="46.5" height="17.25" align-x="426.75" align-y="214.5" 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">X</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:sequence> <ml:real>5</ml:real> <ml:id xml:space="preserve" font="1">...</ml:id> </ml:sequence> </ml:apply> </ml:sequence> </math> <rendering item-idref="15"/> </region> </text> </region> <region region-id="240" left="42" top="228" width="430.5" height="27.75" align-x="42" align-y="240" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Моделирование алгоритма Адамса в системе MathCAD. </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false">(</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false">На примере задачи, решенной выше.)</inlineAttr> </f> </text> </region> <region region-id="967" left="0" top="273" width="6008.25" align-x="8.25" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="" height="170.25"> <area is-collapsed="false" name="" show-name="false" show-border="true" show-icon="true" show-timestamp="true" allow-expand="false" is-locked="false" timestamp="" top-lock-id="967" bottom-lock-id="968" bottom-tag=""> <region region-id="977" left="24" top="282.75" width="173.25" height="13.5" align-x="24" align-y="294" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Данные из п.1.2. Метод Эйлера.</f> </text> </region> <region region-id="969" left="30" top="312.75" width="150.75" height="13.5" align-x="30" align-y="324" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Число точек дискретизации:</f> </text> </region> <region region-id="970" left="186" top="312.75" width="90.75" height="15.75" align-x="201" align-y="324" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">876de2c5220e08cc26d2569da9ad0287</contentHash> <ml:define> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:plus/> <ml:real>10</ml:real> <ml:id xml:space="preserve">FRAME</ml:id> </ml:apply> </ml:define> </ml:provenance> 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Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">d20f025e5ae4d43040e9208e58ddda37</contentHash> <ml:define> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:define> </ml:provenance> </math> <rendering item-idref="29"> <element-image-map> <box left="1.5" top="0.75" width="32.25" height="15.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="991" left="240" top="480.75" width="39" height="17.25" align-x="262.5" align-y="492" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">a058f08175ace154713bb6462de7e2a5</contentHash> <ml:define> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:define> </ml:provenance> </math> <rendering item-idref="30"> <element-image-map> <box left="1.5" top="0.75" width="37.5" height="15.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="992" left="294" top="472.5" width="112.5" height="33.75" align-x="309" align-y="492" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">c6e9e1070d7e11676784a76083a88ee4</contentHash> <ml:define warning="WarnRedefinedUDScalar"> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:minus/> <ml:real>0.5</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>50</ml:real> </ml:apply> <ml:id xml:space="preserve">FRAME</ml:id> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="31"> <element-image-map> <box left="1.5" top="0.75" width="111" height="32.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="246" left="36" top="522.75" width="413.25" height="13.5" align-x="36" align-y="534" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Для проведения анимации необходимо убрать h:=0.1, заменив его на<sp count="2"/>h=0.1</f> </text> </region> <region region-id="247" left="48" top="561" width="96" height="35.25" align-x="66" align-y="582" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">4930de71aaac5437fcea4ec0b007ff1c</contentHash> <ml:define warning="WarnRedefinedBIUnit"> <ml:id xml:space="preserve">K</ml:id> <ml:apply> <ml:id xml:space="preserve">floor</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">b</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="32"> <element-image-map> <box left="1.5" top="0.75" width="94.5" height="33.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="248" left="150" top="570.75" width="51" height="15.75" align-x="165.75" align-y="582" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">420b5f7d18d22667b9bf882a96ee5f55</contentHash> <ml:define> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:real>0</ml:real> <ml:id xml:space="preserve">K</ml:id> </ml:range> </ml:define> </ml:provenance> </math> <rendering item-idref="33"> <element-image-map> <box left="1.5" top="0.75" width="49.5" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="249" left="228" top="570.75" width="66" height="17.25" align-x="245.25" align-y="582" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">0004bb8380aa530fa95312e3e435aa17</contentHash> <ml:define> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">k</ml:id> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="34"> <element-image-map> <box left="1.5" top="0.75" width="64.5" height="15.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="250" left="42" top="600.75" width="174" height="13.5" align-x="42" align-y="612" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Просмотр численного значения:</f> </text> </region> <region region-id="251" left="228" top="600.75" width="39" height="15.75" align-x="244.5" align-y="612" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">1defac042ab898da88f3a9b49edbd193</contentHash> <ml:id xml:space="preserve">K</ml:id> </ml:provenance> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>6</ml:real> </result> </ml:eval> </math> <rendering item-idref="35"> <element-image-map> <box left="1.5" top="0.75" width="8.25" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="252" left="288" top="600.75" width="36.75" height="15.75" align-x="302.25" align-y="612" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">c95ed2ec632c49216273a3314466dd3f</contentHash> <ml:id xml:space="preserve">b</ml:id> </ml:provenance> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>3</ml:real> </result> </ml:eval> </math> <rendering item-idref="36"> <element-image-map> <box left="1.5" top="0.75" width="6" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="253" left="42" top="633" width="450" height="72" align-x="42" align-y="660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Вычисляем значение n-й производной: </f> <region region-id="930" left="255" top="633.75" width="114.75" height="44.25" align-x="303.75" 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:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">Xn</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> </ml:lambda> <ml:degree> <ml:id xml:space="preserve">n</ml:id> </ml:degree> </ml:apply> </ml:apply> </math> <rendering item-idref="37"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> . В системе Maple достаточно предыдущей символьной записи, а в MathCAD - каждую производную надо записывать отдельно:</inlineAttr> </f> </text> </region> <region region-id="254" left="36" top="726.75" width="189.75" height="13.5" align-x="36" align-y="738" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Первая производная уже имеется:</f> </text> </region> <region region-id="255" left="252" top="726" width="97.5" height="16.5" align-x="302.25" align-y="738" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">6b81d1540e84271b9091464db770b08f</contentHash> <ml:define> <ml:function> <ml:id xml:space="preserve">X1</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="38"> <element-image-map> <box left="1.5" top="0.75" width="96" height="15" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="256" left="36" top="780.75" width="123" height="13.5" align-x="36" align-y="792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Вторая производная:<sp count="2"/> </f> </text> </region> <region region-id="257" left="174" top="771" width="229.5" height="36.75" align-x="224.25" align-y="792" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">714dad412eaa74f0e529190bf0ee15e6</contentHash> <ml:define> <ml:function> <ml:id xml:space="preserve">X2</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> <ml:parens> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="39"> <element-image-map> <box left="1.5" top="0.75" width="228" height="35.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="258" left="36" top="816.75" width="121.5" height="13.5" align-x="36" align-y="828" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Третья производная:<sp count="2"/> </f> </text> </region> <region region-id="259" left="42" top="873.75" width="378.75" height="87" align-x="92.25" align-y="900" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">5e3f48440492f58e11a15949ccd7c8cf</contentHash> <ml:define> <ml:function> <ml:id xml:space="preserve">X3</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:parens> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:plus/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:parens> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:define> </ml:provenance> </math> <rendering item-idref="40"> <element-image-map> <box left="1.5" top="0.75" width="377.25" height="85.5" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="260" left="30" top="990.75" width="452.25" height="54" align-x="30" align-y="1002" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Запись последующих производных в MathCAD становится обременительной. В </f> <f family="Arial Cyr" charset="204" size="12">Maple эту процедуру символьного дифференцирования выполняет сама система, </f> <f family="Arial Cyr" charset="204" size="12">что позволяет записывать производные практически любого порядка и вести </f> <f family="Arial Cyr" charset="204" size="12">далее с ними работу.</f> </text> </region> <region region-id="261" left="30" top="1056.75" width="454.5" height="27" align-x="30" align-y="1068" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Можно осуществить проверку<sp count="2"/>правильности </f> <f family="Arial Cyr" charset="204" size="12">вычислен</f> <f family="Arial Cyr" charset="204" size="12">ия производных для выбранных значений функции в отдельных точках:</f> </text> </region> <region region-id="262" left="30" top="1092.75" width="83.25" height="17.25" align-x="90.75" align-y="1104" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">0782eafad0908d9ca3c425e48fbe9527</contentHash> <ml:apply> <ml:id xml:space="preserve">X3</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:sequence> </ml:apply> </ml:provenance> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.9999999999997282</ml:real> </result> </ml:eval> </math> <rendering item-idref="41"> <element-image-map> <box left="1.5" top="0.75" width="52.5" height="15.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="263" left="114" top="1092.75" width="83.25" height="17.25" align-x="174.75" align-y="1104" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">399b8e58e1764d694a9e7c3389f6d971</contentHash> <ml:apply> <ml:id xml:space="preserve">X2</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:sequence> </ml:apply> </ml:provenance> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>2.0000000000000089</ml:real> </result> </ml:eval> </math> <rendering item-idref="42"> <element-image-map> <box left="1.5" top="0.75" width="52.5" height="15.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="264" left="30" top="1116.75" width="352.5" height="13.5" align-x="30" align-y="1128" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Вывод: вычисляет правильно, в том числе и для других функций.</f> </text> </region> <region region-id="265" left="30" top="1146.75" width="122.25" height="13.5" align-x="30" align-y="1158" show-border="false" show-highlight="false" is-protected="true" z-order="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> <f family="Arial Cyr" charset="204" size="12">:</f> </text> </region> <region region-id="266" left="162" top="1146" width="87.75" height="18" align-x="190.5" align-y="1158" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">401cb6538d2e82f56c70c52aa5f49d6d</contentHash> <ml:define warning="WarnRedefinedUDFunction"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X1</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:sequence> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="43"> <element-image-map> <box left="1.5" top="0.75" width="86.25" height="16.5" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> 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</ml:provenance> </math> <rendering item-idref="45"> <element-image-map> <box left="1.5" top="0.75" width="90.75" height="15.75" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="269" left="30" top="1182" width="307.5" height="14.25" align-x="30" align-y="1194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Просмотр численных значений и проверка: </f> </text> </region> <region region-id="270" left="30" top="1206.75" width="49.5" height="17.25" align-x="57" align-y="1218" 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 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branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">0f8c38a9a297f2d7bdbea6831c7b1eb3</contentHash> <ml:define> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">h</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X1</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X2</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:parens> <ml:real>3</ml:real> </ml:apply> <ml:real>6</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X3</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="54"> <element-image-map> <box left="1.5" top="0.75" width="237" height="37.5" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="287" left="30" top="1344.75" width="454.5" height="50.25" align-x="30" align-y="1356" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Значения X</f> <f family="Arial Cyr" charset="204" size="12"> o </f> <f family="Arial Cyr" charset="204" size="12">, X</f> <f family="Arial Cyr" charset="204" size="12"> 1 </f> <f family="Arial Cyr" charset="204" size="12">, X</f> <f family="Arial Cyr" charset="204" size="12"> 2 </f> <f family="Arial Cyr" charset="204" size="12"> необходимы только вначале для запуска алгоритма Адамса.</f> <f family="Arial Cyr" charset="204" size="12">Вычисления последующих X</f> <f family="Arial Cyr" charset="204" size="12">k</f> <f family="Arial Cyr" charset="204" size="12">,<sp count="2"/> </f> <region region-id="888" left="196.5" top="1362" width="30" height="15.75" align-x="210.75" align-y="1373.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">k</ml:id> <ml:real>3</ml:real> </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"> идет автоматически по рекуррентной формуле</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">через разности.</inlineAttr> </f> </text> </region> <region region-id="889" left="36" top="1410" width="176.25" height="14.25" 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branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">8069c0b542a2ed25cb2ea421fdebff19</contentHash> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:sequence> </ml:apply> </ml:provenance> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>2.2916666666666621</ml:real> </result> </ml:eval> </math> <rendering item-idref="58"> <element-image-map> <box left="1.5" top="0.75" width="48" height="16.5" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="893" left="300" top="1440" width="99.75" height="18" align-x="356.25" align-y="1452" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">d3cf8c3870f7eecc1bb7969aed10a353</contentHash> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:sequence> </ml:apply> </ml:provenance> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>4.3333333333332931</ml:real> </result> </ml:eval> </math> <rendering item-idref="59"> <element-image-map> <box left="1.5" top="0.75" width="48" height="16.5" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="894" left="36" top="1464.75" width="99" height="13.5" align-x="36" align-y="1476" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Первые разности:</f> </text> </region> <region region-id="895" left="36" top="1494.75" width="48" height="15.75" align-x="51.75" 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:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="95589038-740e-4125-9372-18f2106d566d" 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xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:sequence> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="61"> <element-image-map> <box left="1.5" top="0.75" width="192" height="16.5" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="897" left="306" top="1494" width="48" height="56.25" align-x="324.75" 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:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:provenance expr-id="1"> <originRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">cb216aa32e4704db2f058b281d3366e8</contentHash> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ΔX1</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:provenance> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:matrix rows="2" cols="1"> <ml:real>1.2916666666666621</ml:real> <ml:real>2.041666666666631</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="62"/> </resultFormat> </math> <rendering item-idref="63"> <element-image-map> <box left="1.5" top="0.75" width="38.25" height="16.5" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="898" left="42" top="1560.75" width="97.5" height="13.5" align-x="42" align-y="1572" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Вторые разности:</f> </text> </region> <region region-id="899" left="42" top="1590.75" width="32.25" height="15.75" align-x="57.75" align-y="1602" 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="95589038-740e-4125-9372-18f2106d566d" 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документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№1\МетодыЭйАдТейСравАнМет.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">b07fc13d151e98825056130b045308cd</contentHash> <ml:define> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Δ2X</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ΔX1</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ΔX1</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="65"> <element-image-map> <box left="1.5" top="0.75" width="148.5" height="16.5" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="901" left="276" top="1590" width="84" height="18" align-x="322.5" align-y="1602" 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 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xmlns="http://schemas.mathsoft.com/provenance10">76594b4b732f0b44eef233cc689e6c15</contentHash> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Δ2X</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:provenance> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.74999999999996891</ml:real> </result> </ml:eval> </math> <rendering item-idref="66"> <element-image-map> <box left="1.5" top="0.75" width="38.25" height="16.5" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="902" left="36" top="1620" width="174" height="14.25" align-x="36" align-y="1632" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Проверка завершена успешно. </f> </text> </region> <region region-id="903" left="36" top="1650.75" width="418.5" height="27" align-x="36" align-y="1662" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Далее все последующие значения "х" будем вычислять по формуле Адамса,</f> <f family="Arial Cyr" charset="204" size="12">имеющей вид:</f> </text> </region> <region region-id="904" left="42" top="1698.75" width="51" height="15.75" align-x="57.75" align-y="1710" 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="95589038-740e-4125-9372-18f2106d566d" version-id="1e4dc304-7159-4323-adf1-d951fe5f56ca" branch-id="00000000-0000-0000-0000-000000000000" revision-num="26" is-modified="true" 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<ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>23</ml:real> <ml:id xml:space="preserve">h</ml:id> </ml:apply> <ml:real>12</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:sequence> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">h</ml:id> </ml:apply> <ml:real>3</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:sequence> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>5</ml:real> <ml:id xml:space="preserve">h</ml:id> </ml:apply> <ml:real>12</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ψ</ml:id> <ml:sequence> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:sequence> </ml:apply> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="68"> <element-image-map> <box left="1.5" top="0.75" width="365.25" height="32.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="906" left="42" top="1734.75" width="423.75" height="13.5" align-x="42" align-y="1746" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Результаты вычислений представим в виде вектора X и графически на рис. 3</f> </text> </region> <region region-id="907" left="48" top="1770.75" width="327.75" height="21.75" align-x="70.5" align-y="1788" 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 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<inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">) </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">Решить уравнение x'=cos(x) при условии х(0)=0 методом Адамса.</f> <f family="Arial Cyr" charset="204" size="12">Полученные решения сравнить с точными решениями, полученными, например, с по-</f> <f family="Arial Cyr" charset="204" size="12">мощью опции Bulstoer, или dsolve, или Mathematica. </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="1024" left="36" top="2502.75" width="415.5" height="27" align-x="36" align-y="2514" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">У студентов трудности вызывает 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