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📄 第四节 用mathematica解方程和作级数运算.htm

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style="mso-text-raise: -12.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1037         
style="HEIGHT: 30.75pt; WIDTH: 195.75pt" o:ole="" type="#_x0000_t75">         
<V:IMAGEDATA o:title=""         
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image023.wmz"></V:SHAPE><![endif]--><IMG src="images/4.htm7.gif"         
v:shapes="_x0000_i1037" width="261" height="41"></SPAN><!--[if gte mso 9]><xml>        
 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1037"        
  DrawAspect="Content" ObjectID="_1048959549">        
 </o:OLEObject>        
</xml><![endif]-->         
</b></font>         
</SPAN></P>        
<P class=MsoNormal style="line-height: 200%"><SPAN         
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><b><font size="4">（</font></b></SPAN><b><font size="4"><SPAN         
lang=EN-US>6</SPAN><SPAN         
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">）</SPAN><SPAN         
lang=EN-US>In[9]:=Solve[{x^2 + y^2 + 4x - 2y + 3 = = 0</SPAN><SPAN           
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN><SPAN          
lang=EN-US> x^2 + 4x*y - y^2 + 10y - 9 = = 0}</SPAN><SPAN           
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN><SPAN          
lang=EN-US> {x</SPAN><SPAN           
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN><SPAN          
lang=EN-US> y}]</SPAN></font></b></P>          
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><font size="4"><b>Out[9]=<SPAN         
style="mso-text-raise: -21.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1038         
style="HEIGHT: 48pt; WIDTH: 378pt" o:ole="" type="#_x0000_t75"> <V:IMAGEDATA         
o:title=""         
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image025.wmz"></V:SHAPE><![endif]--><IMG src="images/4.htm8.gif"         
v:shapes="_x0000_i1038" width="504" height="64"></SPAN><!--[if gte mso 9]><xml>        
 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1038"        
  DrawAspect="Content" ObjectID="_1048959550">        
 </o:OLEObject>        
</xml><![endif]-->         
</b></font>         
</SPAN></P>        
<P class=MsoNormal style="line-height: 200%"><SPAN         
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><b><font size="4">（</font></b></SPAN><b><font size="4"><SPAN         
lang=EN-US>7</SPAN><SPAN         
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">）</SPAN><SPAN         
lang=EN-US> In[10]:=Solve[{x1 + x2 + x3 + x4 + x5 = = 0</SPAN><SPAN           
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN><SPAN          
lang=EN-US> 3x1 + 2x2 + x3 + x4 - 3x5 = = 0</SPAN><SPAN           
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN>          
<SPAN lang=EN-US>x2 + 2x3 + 2x4 + 6x5 = = 0</SPAN><SPAN           
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN><SPAN          
lang=EN-US> 5x1 + 4x2 + 3x3 + 3x4 - x5 = = 0}</SPAN><SPAN           
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN><SPAN          
lang=EN-US> {x1</SPAN><SPAN           
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN><SPAN          
lang=EN-US> x2</SPAN><SPAN           
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN><SPAN          
lang=EN-US> x3</SPAN><SPAN           
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN>          
<SPAN lang=EN-US>x4</SPAN><SPAN           
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN><SPAN          
lang=EN-US> x5}]</SPAN></font></b></P>          
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN         
lang=EN-US>Solve</SPAN><SPAN         
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">：：</SPAN><SPAN         
lang=EN-US>svars</SPAN><SPAN         
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">：</SPAN><SPAN         
lang=EN-US>Equations may not give solutions for all "solve"</SPAN></b></font></P>          
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN          
lang=EN-US><font size="4"><b>variables.</b></font></SPAN></P>        
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN lang=EN-US>Out[10]={{x1         
-&gt; x3 + x4 + 5 x5</SPAN><SPAN         
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN><SPAN         
lang=EN-US> x2 -&gt; -2 x3 - 2 x4 - 6 x5}}</SPAN></b></font></P>          
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN          
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><font size="4"><b>上述结果表明，虽然方程组不能给出具体解，但仍会给出方程组的一般解。</b></font></SPAN></P>        
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%">　</P>        
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%">　</P>        
<P class=MsoNormal style="line-height: 200%"><SPAN         
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><b><font color="#FF0000" size="5">二、<a name="常微分方程">常微分方程</a></font></b></SPAN></P>      
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN       
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">解常微分方程实际上就是求满足方程的某函数</SPAN><SPAN       
lang=EN-US>y[x]</SPAN><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">。在</SPAN><SPAN      
lang=EN-US>Mathematica4.0</SPAN><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">中，其导数用</SPAN><SPAN      
lang=EN-US>y’[x]</SPAN><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">、</SPAN><SPAN      
lang=EN-US>y’’[x]</SPAN><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">等来表示。</SPAN></b></font></P>     
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">求解常微分方程主要由函数</SPAN><SPAN      
lang=EN-US>DSolve</SPAN><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">来完成。以下给出其使用格式：</SPAN></b></font></P>     
<TABLE border=1 cellPadding=0 cellSpacing=0      
style="border-collapse: collapse; mso-table-layout-alt: fixed; mso-border-alt: solid windowtext .75pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; border-style: none; border-width: medium" width="699">     
  <TBODY>     
  <TR>     
    <TD      
    style="border: 0.75pt solid windowtext; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; padding-bottom: 0cm"      
    vAlign=top width=343>     
      <P align=center class=MsoNormal style="text-align: center; line-height: 200%"><SPAN      
      style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><font size="4"><b>格式</b></font></SPAN></P></TD>     
    <TD      
    style="mso-border-left-alt: solid windowtext .75pt; border-left-style: none; border-left-width: medium; border-right: 0.75pt solid windowtext; border-top: 0.75pt solid windowtext; border-bottom: 0.75pt solid windowtext; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; padding-bottom: 0cm"      
    vAlign=top width=325>     
      <P align=center class=MsoNormal style="text-align: center; line-height: 200%"><SPAN      
      style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><font size="4"><b>含义</b></font></SPAN></P></TD></TR>     
  <TR>     
    <TD      
    style="mso-border-top-alt: solid windowtext .75pt; border-left: 0.75pt solid windowtext; border-right: 0.75pt solid windowtext; border-top-style: none; border-top-width: medium; border-bottom: 0.75pt solid windowtext; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; padding-bottom: 0cm"      
    vAlign=top width=343>     
      <P class=MsoNormal style="line-height: 200%"><SPAN lang=EN-US><b><font size="4">DSolve[eqns</font></b></SPAN><b><font size="4"><SPAN      
      style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN><SPAN      
      lang=EN-US>y[x]</SPAN><SPAN      
      style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN><SPAN      
      lang=EN-US>x]</SPAN></font></b></P></TD>     
    <TD      
    style="mso-border-left-alt: solid windowtext .75pt; mso-border-top-alt: solid windowtext .75pt; border-left-style: none; border-left-width: medium; border-right: 0.75pt solid windowtext; border-top-style: none; border-top-width: medium; border-bottom: 0.75pt solid windowtext; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; padding-bottom: 0cm"      
    vAlign=top width=325>     
      <P class=MsoNormal style="line-height: 200%"><SPAN      
      style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><b><font size="4">求解微分方程</font></b></SPAN><b><font size="4"><SPAN      
      lang=EN-US>eqns</SPAN><SPAN      
      style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，其中</SPAN><SPAN      
      lang=EN-US>y[x]</SPAN><SPAN      
      style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">为</SPAN><SPAN      
      lang=EN-US>x</SPAN><SPAN      
      style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">的函数</SPAN></font></b></P></TD></TR>     
  <TR>     
    <TD      
    style="mso-border-top-alt: solid windowtext .75pt; border-left: 0.75pt solid windowtext; border-right: 0.75pt solid windowtext; border-top-style: none; border-top-width: medium; border-bottom: 0.75pt solid windowtext; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; padding-bottom: 0cm"      
    vAlign=top width=343>     
      <P class=MsoNormal style="line-height: 200%"><SPAN lang=EN-US><b><font size="4">DSolve[eqns</font></b></SPAN><b><font size="4"><SPAN      
      style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN><SPAN      
      lang=EN-US>y</SPAN><SPAN      
      style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN><SPAN      
      lang=EN-US>x]</SPAN></font></b></P></TD>     
    <TD      
    style="mso-border-left-alt: solid windowtext .75pt; mso-border-top-alt: solid windowtext .75pt; border-left-style: none; border-left-width: medium; border-right: 0.75pt solid windowtext; border-top-style: none; border-top-width: medium; border-bottom: 0.75pt solid windowtext; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; padding-bottom: 0cm"      
    vAlign=top width=325>     
      <P class=MsoNormal style="line-height: 200%"><SPAN      
      style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><b><font size="4">求解微分方程</font></b></SPAN><b><font size="4"><SPAN      
      lang=EN-US>eqns</SPAN><SPAN      
      style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，其中</SPAN><SPAN      
      lang=EN-US>y[x]</SPAN><SPAN      
      style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">为</SPAN><SPAN      
      lang=EN-US>x</SPAN><SPAN      
      style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">的函数</SPAN></font></b></P></TD></TR>     
  <TR>     
    <TD      
    style="mso-border-top-alt: solid windowtext .75pt; border-left: 0.75pt solid windowtext; border-right: 0.75pt solid windowtext; border-top-style: none; border-top-width: medium; border-bottom: 0.75pt solid windowtext; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; padding-bottom: 0cm"
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