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📄 第四节 用mathematica解方程和作级数运算.htm

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style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">（</SPAN><SPAN         
lang=EN-US>2</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[3]:=Solve[x^2 + a*x + 2 = = 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></b></font></P>          
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN         
lang=EN-US>Out[3]=</SPAN><SPAN lang=EN-US         
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"> </SPAN><SPAN lang=EN-US         
style="mso-text-raise: -12.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1031         
style="HEIGHT: 30.75pt; WIDTH: 270pt" o:ole="" type="#_x0000_t75"><V:IMAGEDATA         
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v:shapes="_x0000_i1031" width="360" height="41"></SPAN><SPAN lang=EN-US         
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><!--[if gte mso 9]><xml>        
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<O:P></O:P></SPAN></b></font></P>        
<P class=MsoNormal style="text-indent: 20.5pt; 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; mso-bidi-font-size: 10.0pt">由于</SPAN><SPAN         
lang=EN-US style="mso-bidi-font-size: 10.0pt">a</SPAN><SPAN         
style="font-family: 宋体; mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman; mso-bidi-font-size: 10.0pt">不是方程的未知量，所以被当作常数来处理。</SPAN></b></font></P>        
<P class=MsoNormal style="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'">（</SPAN><SPAN         
lang=EN-US>3</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[4]:=Solve[x^3 + x^2 - 10 = = 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></b></font></P>          
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN         
lang=EN-US>Out[4]=</SPAN><SPAN lang=EN-US         
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"> </SPAN><SPAN lang=EN-US         
style="mso-text-raise: -44.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1032         
style="HEIGHT: 96pt; WIDTH: 5in" o:ole="" type="#_x0000_t75"><V:IMAGEDATA         
o:title=""         
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image013.wmz"></V:SHAPE><![endif]--><IMG src="images/4.htm2.gif"         
v:shapes="_x0000_i1032" width="480" height="128"></SPAN><SPAN lang=EN-US         
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><!--[if gte mso 9]><xml>        
 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1032"        
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</SPAN><SPAN lang=EN-US style="mso-spacerun: yes">&nbsp;</SPAN></b></font></P>        
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN         
lang=EN-US><b><font size="4">In[5]:=NSolve[x^3 + x^2 - 10 = = 0</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> x]</SPAN></font></b></P>          
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN lang=EN-US>Out[5]={{x         
-&gt; -1.43373 - 1.81639i}</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 -&gt; -1.43373 +1.81639 i}</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 -&gt; 1.86746}}</SPAN></b></font></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>4</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[6]:=Solve[x^6 - 1 = = 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></font></b></P>          
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN          
lang=EN-US><font size="4"><b>Out[6]=</b></font></SPAN></P>        
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN lang=EN-US>{{x -&gt;         
-1}</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 -&gt;1}</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 -&gt;<SPAN           
style="mso-text-raise: -5.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1033          
style="HEIGHT: 18pt; WIDTH: 42.75pt" o:ole="" type="#_x0000_t75"> <V:IMAGEDATA          
o:title=""          
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image015.wmz"></V:SHAPE><![endif]--><IMG src="images/4.htm3.gif"          
v:shapes="_x0000_i1033" width="57" height="24"></SPAN><!--[if gte mso 9]><xml>         
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</xml><![endif]-->          
}</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 -&gt;<SPAN           
style="mso-text-raise: -5.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1034          
style="HEIGHT: 18pt; WIDTH: 33.75pt" o:ole="" type="#_x0000_t75"> <V:IMAGEDATA          
o:title=""          
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image017.wmz"></V:SHAPE><![endif]--><IMG src="images/4.htm4.gif"          
v:shapes="_x0000_i1034" width="45" height="24"></SPAN><!--[if gte mso 9]><xml>         
 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1034"         
  DrawAspect="Content" ObjectID="_1048959546">         
 </o:OLEObject>         
</xml><![endif]-->          
}</SPAN><SPAN           
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN></b></font></P>         
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><b><font size="4">{x -&gt;<SPAN           
style="mso-text-raise: -5.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1035          
style="HEIGHT: 18pt; WIDTH: 45pt" o:ole="" type="#_x0000_t75"> <V:IMAGEDATA          
o:title=""          
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image019.wmz"></V:SHAPE><![endif]--><IMG src="images/4.htm5.gif"          
v:shapes="_x0000_i1035" width="60" height="24"></SPAN><!--[if gte mso 9]><xml>         
 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1035"         
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}</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>{x -&gt;<SPAN style="mso-text-raise: -5.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1036           
style="HEIGHT: 18pt; WIDTH: 36pt" o:ole="" type="#_x0000_t75"> <V:IMAGEDATA          
o:title=""          
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image021.wmz"></V:SHAPE><![endif]--><IMG src="images/4.htm6.gif"          
v:shapes="_x0000_i1036" width="48" height="24"></SPAN><!--[if gte mso 9]><xml>         
 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1036"         
  DrawAspect="Content" ObjectID="_1048959548">         
 </o:OLEObject>         
</xml><![endif]-->          
}}</SPAN></font></b></P>          
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN         
lang=EN-US>In[7]:=NSolve[x^6 - 1 = = 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></b></font></P>          
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN lang=EN-US>Out[7]={{x         
-&gt; -1.}</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 -&gt; -0.5 - 0.866025 i}</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 -&gt; -0.5 + 0.866025i}</SPAN><SPAN           
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN></b></font></P>         
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><b><font size="4">{x -&gt; 0.5 -           
0.866025i}</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> {x -&gt; 0.5 + 0.866025i}</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 -&gt; 1.}}</SPAN></font></b></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>5</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[8]:=Solve[{a*x + b*y = = m</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> c*x + d*y = = n}</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[8]=<SPAN
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