📄 第四节 用mathematica解方程和作级数运算.htm
字号:
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>{<SPAN
style="mso-text-raise: -5.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1039
style="HEIGHT: 17.25pt; WIDTH: 12.75pt" o:ole="" type="#_x0000_t75">
<V:IMAGEDATA o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image027.wmz"></V:SHAPE><![endif]--><IMG src="images/4.htm9.gif"
v:shapes="_x0000_i1039" width="17" height="23"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1039"
DrawAspect="Content" ObjectID="_1048959551">
</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><SPAN
lang=EN-US><SPAN
style="mso-text-raise: -5.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1040
style="HEIGHT: 17.25pt; WIDTH: 15pt" o:ole="" type="#_x0000_t75">
<V:IMAGEDATA o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image029.wmz"></V:SHAPE><![endif]--><IMG src="images/4.htm10.gif"
v:shapes="_x0000_i1040" width="20" height="23"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1040"
DrawAspect="Content" ObjectID="_1048959552">
</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><SPAN
lang=EN-US>…}</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">求解微分方程组，其中</font></b></SPAN><b><font size="4"><SPAN
lang=EN-US><SPAN
style="mso-text-raise: -5.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1041
style="HEIGHT: 17.25pt; WIDTH: 12.75pt" o:ole="" type="#_x0000_t75">
<V:IMAGEDATA o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image027.wmz"></V:SHAPE><![endif]--><IMG src="images/4.htm11.gif"
v:shapes="_x0000_i1041" width="17" height="23"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1041"
DrawAspect="Content" ObjectID="_1048959553">
</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><SPAN
lang=EN-US><SPAN
style="mso-text-raise: -5.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1042
style="HEIGHT: 17.25pt; WIDTH: 15pt" o:ole="" type="#_x0000_t75">
<V:IMAGEDATA o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image029.wmz"></V:SHAPE><![endif]--><IMG src="images/4.htm12.gif"
v:shapes="_x0000_i1042" width="20" height="23"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1042"
DrawAspect="Content" ObjectID="_1048959554">
</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><SPAN
lang=EN-US>…</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></TBODY></TABLE>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><b><font size="4">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'">的表现形式为：</SPAN></font></b></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><font size="4"><b>lhs1=
=rhs1</b></font></SPAN></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'"><b><font size="4">函数</font></b></SPAN><b><font size="4"><SPAN
lang=EN-US>DSolve[eqns</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'">，</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'">算出的是一个函数形式，不是函数表达式。它不能参加运算。例如：</SPAN></font></b></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><font size="4"><b> <O:P>
</O:P></b></font></SPAN></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><b><font size="4">In[11]:=DSolve[y'[x] + y[x] = = 2</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>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN lang=EN-US>Out[11]=
{{y[x]->2+<SPAN style="mso-text-raise: -3.0pt"><!--[if gte vml 1]><V:SHAPE
id=_x0000_i1043 style="HEIGHT: 15.75pt; WIDTH: 18pt" o:ole=""
type="#_x0000_t75"> <V:IMAGEDATA o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image033.wmz"></V:SHAPE><![endif]--><IMG src="images/4.htm13.gif"
v:shapes="_x0000_i1043" width="24" height="21"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1043"
DrawAspect="Content" ObjectID="_1048959555">
</o:OLEObject>
</xml><![endif]-->
C[1]}}<SPAN style="mso-spacerun: yes"> </SPAN></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[1]</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">为常数，以下同</SPAN><SPAN
lang=EN-US>*</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%"><font size="4"><b><font color="#0000FF"><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">上</SPAN><span style="font-family: 宋体; mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman">述输出仅给出y[x]<SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">的一个形式或符号</SPAN></span></font><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">。它并不代表一个函数，不能把它当作函数进行求值及参加其它运算。使用替换操作可发现：</SPAN></b></font></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><font size="4"><b>In[12]:=y[x] +
2y'[x] + y[12] /. %</b></font></SPAN></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><font size="4"><b>Out[12]={2+<SPAN
style="mso-text-raise: -3.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1044
style="HEIGHT: 15.75pt; WIDTH: 18pt" o:ole="" type="#_x0000_t75"> <V:IMAGEDATA
o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image035.wmz"></V:SHAPE><![endif]--><IMG src="images/4.htm14.gif"
v:shapes="_x0000_i1044" width="24" height="21"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1044"
DrawAspect="Content" ObjectID="_1048959556">
</o:OLEObject>
</xml><![endif]-->
C[1]+y[12]+2y’[x]}</b></font></SPAN></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><font size="4"><b>In[13]:=y'[x] +
y[x] = = 2 /. %%</b></font></SPAN></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><font size="4"><b>Out[13]={2+<SPAN
style="mso-text-raise: -3.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1045
style="HEIGHT: 15.75pt; WIDTH: 18pt" o:ole="" type="#_x0000_t75"> <V:IMAGEDATA
o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image035.wmz"></V:SHAPE><![endif]--><IMG src="images/4.htm15.gif"
v:shapes="_x0000_i1045" width="24" height="21"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1045"
DrawAspect="Content" ObjectID="_1048959557">
</o:OLEObject>
</xml><![endif]-->
C[1]+y’[x]= =2}</b></font></SPAN></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font color="#0000FF"><span style="font-family: 宋体; mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman"><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><b><font size="4">替换过程中，对</font></b></SPAN><b><font size="4">y'[x]<SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">没有影响，仍输出</SPAN>y'[x]<SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">。以下使用</SPAN>y<SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">求解</SPAN></font></b></span></font><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></font></b></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><b><font size="4">In[14]:=DSolve[y'[x] + y[x] = = 2</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⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -