範例：新增解題指令群的單位

解題指令群 > 範例：新增解題指令群的單位

範例：新增解題指令群的單位

您可以新增解題指令群的單位。您必須確定整個計算的單位彼此相容。

1. 定義單擺的長度。

2. 插入解題指令群、定義問題的微分方程式，並使用 odesolve 函數求解方程式。角度 Ɵ 是垂直線與單擺之間的角度。

<region id="ID0ECTRKB" actualWidth="233" actualHeight="221.39999999999998" top="230.40000000000003" left="38.400000000000006" height="221.39999999999998" width="233" xmlns="http://schemas.mathsoft.com/worksheet50">
 <solveblock>
 <regions>
 <region id="" actualWidth="174.87333333333333" actualHeight="56.369333557128911" top="43.2" left="24" solve-block-category="constraint">
 <math resultRef="92">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <equal />
 <apply>
 <derivative />
 <lambda>
 <boundVars>
 <id xml:space="preserve">t</id>
 </boundVars>
 <apply>
 <id xml:space="preserve">θ</id>
 <id xml:space="preserve">t</id>
 </apply>
 </lambda>
 <degree>
 <real>2</real>
 </degree>
 </apply>
 <apply>
 <mult />
 <apply>
 <neg />
 <apply>
 <div />
 <id labels="UNIT" xml:space="preserve">g</id>
 <id xml:space="preserve">l</id>
 </apply>
 </apply>
 <apply>
 <id xml:space="preserve">sin</id>
 <apply>
 <id xml:space="preserve">θ</id>
 <id xml:space="preserve">t</id>
 </apply>
 </apply>
 </apply>
 </apply>
 </math>
 </region>
 <region id="" actualWidth="61.693333333333342" actualHeight="25.6" top="96" left="24" solve-block-category="constraint">
 <math resultRef="94">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <equal />
 <apply>
 <id xml:space="preserve">θ</id>
 <real>0</real>
 </apply>
 <real>0</real>
 </apply>
 </math>
 </region>
 <region id="" actualWidth="64.786666666666676" actualHeight="25.6" top="144" left="24" solve-block-category="constraint">
 <math resultRef="96">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <equal />
 <apply>
 <apply>
 <functionDerivative />
 <id xml:space="preserve">θ</id>
 </apply>
 <real>0</real>
 </apply>
 <real>2</real>
 </apply>
 </math>
 </region>
 <region id="" actualWidth="164.43666666666667" actualHeight="25.6" top="196.8" left="24" solve-block-category="solver">
 <math resultRef="98">
 <define xmlns="http://schemas.mathsoft.com/math50">
 <id labels="VARIABLE" xml:space="preserve">Θ</id>
 <apply>
 <id labels="KEYWORD" xml:space="preserve">odesolve</id>
 <sequence>
 <apply>
 <id xml:space="preserve">θ</id>
 <id xml:space="preserve">t</id>
 </apply>
 <real>10</real>
 </sequence>
 </apply>
 </define>
 </math>
 </region>
 </regions>
 </solveblock>
</region>

長度 l 與重力常數 g 的單位如下：

但是，初始條件與終點沒有單位。因此，會出現單位相容性錯誤。

3. 新增所有解題指令群元件的相容單位。

<region id="ID0ERVRKB" actualWidth="233" actualHeight="223" top="614.40000000000009" left="38.400000000000006" height="223" width="233" xmlns="http://schemas.mathsoft.com/worksheet50">
 <solveblock>
 <regions>
 <region id="" actualWidth="174.87333333333333" actualHeight="56.369333557128911" top="43.2" left="24" solve-block-category="constraint">
 <math resultRef="102">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <equal />
 <apply>
 <derivative />
 <lambda>
 <boundVars>
 <id xml:space="preserve">t</id>
 </boundVars>
 <apply>
 <id xml:space="preserve">θ</id>
 <id xml:space="preserve">t</id>
 </apply>
 </lambda>
 <degree>
 <real>2</real>
 </degree>
 </apply>
 <apply>
 <mult />
 <apply>
 <neg />
 <apply>
 <div />
 <id labels="UNIT" xml:space="preserve">g</id>
 <id xml:space="preserve">l</id>
 </apply>
 </apply>
 <apply>
 <id xml:space="preserve">sin</id>
 <apply>
 <id xml:space="preserve">θ</id>
 <id xml:space="preserve">t</id>
 </apply>
 </apply>
 </apply>
 </apply>
 </math>
 </region>
 <region id="" actualWidth="73.346666666666678" actualHeight="25.6" top="96" left="24" solve-block-category="constraint">
 <math resultRef="104">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <equal />
 <apply>
 <id xml:space="preserve">θ</id>
 <apply>
 <scale />
 <real>0</real>
 <id xml:space="preserve">s</id>
 </apply>
 </apply>
 <real>0</real>
 </apply>
 </math>
 </region>
 <region id="" actualWidth="104.56" actualHeight="29.752000000000002" top="144" left="24" solve-block-category="constraint">
 <math resultRef="106">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <equal />
 <apply>
 <apply>
 <functionDerivative />
 <id xml:space="preserve">θ</id>
 </apply>
 <apply>
 <scale />
 <real>0</real>
 <id xml:space="preserve">s</id>
 </apply>
 </apply>
 <apply>
 <mult />
 <real>2</real>
 <apply>
 <pow />
 <id xml:space="preserve">s</id>
 <real>-1</real>
 </apply>
 </apply>
 </apply>
 </math>
 </region>
 <region id="" actualWidth="176.67666666666668" actualHeight="25.6" top="196.8" left="24" solve-block-category="solver">
 <math resultRef="108">
 <define xmlns="http://schemas.mathsoft.com/math50">
 <id labels="VARIABLE" xml:space="preserve">Θ</id>
 <apply>
 <id labels="KEYWORD" xml:space="preserve">odesolve</id>
 <sequence>
 <apply>
 <id labels="UNIT" xml:space="preserve" label-is-contextual="true">θ</id>
 <id xml:space="preserve">t</id>
 </apply>
 <apply>
 <scale />
 <real>10</real>
 <id labels="UNIT" xml:space="preserve" label-is-contextual="true">s</id>
 </apply>
 </sequence>
 </apply>
 </define>
 </math>
 </region>
 </regions>
 </solveblock>
</region>

4. 定義要繪製解題指令群之解的值域。您必須使用步距範圍運算子定義含有單位的值域。

5. 繪製解題指令群的解。

6. 構建解題指令群，然後使用 minimize 函數尋找當提供的估值為 t=5 s 時，何時 Ɵ 最小。

<region id="ID0EU1RKB" actualWidth="300" actualHeight="100" top="1209.6000000000001" left="38.400000000000006" height="100" width="300" xmlns="http://schemas.mathsoft.com/worksheet50">
 <solveblock>
 <regions>
 <region id="" actualWidth="50.683333333333337" actualHeight="25.6" top="38.400000000000006" left="19.200000000000003" solve-block-category="guess-value">
 <math resultRef="127">
 <define xmlns="http://schemas.mathsoft.com/math50">
 <id labels="VARIABLE" xml:space="preserve">t</id>
 <apply>
 <scale />
 <real>5</real>
 <id labels="UNIT" xml:space="preserve" label-is-contextual="true">s</id>
 </apply>
 </define>
 </math>
 </region>
 <region id="" actualWidth="218.85999999999999" actualHeight="27.791200000000003" top="76.800000000000082" left="19.200000000000003" solve-block-category="solver">
 <math resultRef="129">
 <define xmlns="http://schemas.mathsoft.com/math50">
 <id labels="*" xml:space="preserve">
 t<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">min</Subscript>
 </id>
 <eval>
 <apply>
 <id labels="KEYWORD" xml:space="preserve">minimize</id>
 <sequence>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">Θ</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">t</id>
 </sequence>
 </apply>
 <unitOverride>
 <placeholder />
 </unitOverride>
 </eval>
 </define>
 </math>
 </region>
 </regions>
 </solveblock>
</region>

估值的單位必須與要最小化之函數的定義相容。

7. 構建解題指令群，然後使用 maximize 函數尋找當提供的估值為 t=2 s 且約束條件為 t<4 s 時，何時 Ɵ 最大。

<region id="ID0E63RKB" actualWidth="311.96333333333337" actualHeight="135" top="1440.0000000000002" left="38.400000000000006" height="135" width="311.96333333333337" xmlns="http://schemas.mathsoft.com/worksheet50">
 <solveblock>
 <regions>
 <region id="" actualWidth="50.683333333333337" actualHeight="25.6" top="38.400000000000006" left="19.200000000000003" solve-block-category="guess-value">
 <math resultRef="131">
 <define xmlns="http://schemas.mathsoft.com/math50">
 <id labels="VARIABLE" xml:space="preserve">t</id>
 <apply>
 <scale />
 <real>2</real>
 <id labels="UNIT" xml:space="preserve" label-is-contextual="true">s</id>
 </apply>
 </define>
 <resultFormat>
 <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
 </resultFormat>
 </math>
 </region>
 <region id="" actualWidth="48.513333333333335" actualHeight="25.6" top="76.800000000000011" left="19.200000000000003" solve-block-category="constraint">
 <math resultRef="133">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <lessThan />
 <id labels="VARIABLE" xml:space="preserve">t</id>
 <apply>
 <scale />
 <real>4</real>
 <id labels="UNIT" xml:space="preserve" label-is-contextual="true">s</id>
 </apply>
 </apply>
 <resultFormat>
 <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
 </resultFormat>
 </math>
 </region>
 <region id="" actualWidth="223.94666666666669" actualHeight="27.791200000000003" top="115.20000000000002" left="19.200000000000003" solve-block-category="solver">
 <math resultRef="135">
 <define xmlns="http://schemas.mathsoft.com/math50">
 <id labels="*" xml:space="preserve">
 t<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">max</Subscript>
 </id>
 <eval>
 <apply>
 <id labels="KEYWORD" xml:space="preserve">maximize</id>
 <sequence>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">Θ</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">t</id>
 </sequence>
 </apply>
 <unitOverride>
 <placeholder />
 </unitOverride>
 </eval>
 </define>
 <resultFormat>
 <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
 </resultFormat>
 </math>
 </region>
 </regions>
 </solveblock>
</region>

8. 使用 SIUnitsOf 函數移除最大點與最小點的單位。在使用無單位的垂直標記時需要此函數。

<region id="ID0E55RKB" actualWidth="230.05666666666667" actualHeight="51.582400000000007" top="1689.6000000000004" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
 <math resultRef="137">
 <define xmlns="http://schemas.mathsoft.com/math50">
 <id labels="VARIABLE" xml:space="preserve">max</id>
 <eval>
 <apply>
 <div />
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
 t<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">max</Subscript>
 </id>
 <apply>
 <id labels="FUNCTION" xml:space="preserve">SIUnitsOf</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
 t<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">max</Subscript>
 </id>
 </apply>
 </apply>
 <unitOverride>
 <placeholder />
 </unitOverride>
 </eval>
 </define>
 </math>
</region>

<region id="ID0EM6RKB" actualWidth="226.24666666666664" actualHeight="51.582400000000007" top="1766.4000000000003" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
 <math resultRef="139">
 <define xmlns="http://schemas.mathsoft.com/math50">
 <id labels="VARIABLE" xml:space="preserve">min</id>
 <eval>
 <apply>
 <div />
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
 t<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">min</Subscript>
 </id>
 <apply>
 <id labels="FUNCTION" xml:space="preserve">SIUnitsOf</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
 t<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">min</Subscript>
 </id>
 </apply>
 </apply>
 <unitOverride>
 <placeholder />
 </unitOverride>
 </eval>
 </define>
 </math>
</region>

9. 顯示原始繪圖上的最大點與最小點。使用垂直標記顯示這兩點與時間軸的相交處。

<region id="ID0E3ASKB" actualWidth="577.2" actualHeight="244.80000000000004" top="1881.6000000000004" left="38.400000000000006" height="244.80000000000004" width="577.2" xmlns="http://schemas.mathsoft.com/worksheet50">
 <plot background-type="white" origin-positioning="true">
 <xyPlot>
 <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
 <legend />
 <traces>
 <trace resultRef="141">
 <traceStyle color="#FF00008B" symbol="none" line-weight="1" line-style="Solid">lines</traceStyle>
 </trace>
 <trace resultRef="142">
 <traceStyle color="#FFFF0000" symbol="filledRectangle" line-weight="2" line-style="Solid">lines</traceStyle>
 </trace>
 <trace resultRef="143">
 <traceStyle color="#FF068149" symbol="filledStar" line-weight="2" line-style="Solid">線條</traceStyle>
 </trace>
 </traces>
 <graph-size width="442.8" height="110.4" />
 <axes>
 <xAxis rank="1" legend-position="PlotBoundaryBottom" start="0" end="10">
 <axisLine position="origin" positionticmark="2" legendWidth="81.8666666666667" />
 <axisGrid>
 <gridFrequency>11</gridFrequency>
 <gridLabels display="true" />
 <gridLines />
 <tickMarks display="true" />
 </axisGrid>
 <axisLabel />
 <markers>
 <marker resultRef="144" display="true" color="#FF068149" line-style="Dash" value="2.4368823377188966">
 <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">max</id>
 </marker>
 <marker resultRef="146" display="true" color="#FFED1D2F" line-style="Dash" value="5.3611508941582011">
 <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">min</id>
 </marker>
 </markers>
 <numberFormat>
 <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" />
 </numberFormat>
 <plotEquations>
 <plotEquation>
 <math resultRef="148">
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">t</id>
 </math>
 <math resultRef="149">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 <plotEquation>
 <math resultRef="150">
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">
 t<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">min</Subscript>
 </id>
 </math>
 <math resultRef="151">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 <plotEquation>
 <math resultRef="152">
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">
 t<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">max</Subscript>
 </id>
 </math>
 <math resultRef="153">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 </plotEquations>
 <xyDomain scale-type="linear" auto-scale="true">
 <startValue>
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </startValue>
 <endValue>
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </endValue>
 </xyDomain>
 </xAxis>
 <yAxis rank="1" legend-position="PlotBoundaryLeft" start="-0.8" end="0.8">
 <axisLine position="origin" positionticmark="0" legendWidth="105.763333333333" />
 <axisGrid>
 <gridFrequency>5</gridFrequency>
 <gridLabels display="true" />
 <gridLines />
 <tickMarks display="true" />
 </axisGrid>
 <axisLabel />
 <markers />
 <numberFormat>
 <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" />
 </numberFormat>
 <plotEquations>
 <plotEquation>
 <math resultRef="158">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">Θ</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">t</id>
 </apply>
 </math>
 <math resultRef="159">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 <plotEquation>
 <math resultRef="160">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">Θ</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
 t<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">min</Subscript>
 </id>
 </apply>
 </math>
 <math resultRef="161">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 <plotEquation>
 <math resultRef="162">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">Θ</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
 t<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">max</Subscript>
 </id>
 </apply>
 </math>
 <math resultRef="163">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 </plotEquations>
 <xyDomain scale-type="linear" auto-scale="true">
 <startValue resultRef="155">
 <real xmlns="http://schemas.mathsoft.com/math50">-0.8</real>
 </startValue>
 <secondTickValue resultRef="157">
 <real xmlns="http://schemas.mathsoft.com/math50">-0.4</real>
 </secondTickValue>
 <endValue>
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </endValue>
 </xyDomain>
 </yAxis>
 </axes>
 </xyPlot>
 </plot>
</region>

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