📄 第三节 用mathematica作积分计算.htm
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<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'">积分</SPAN><SPAN
lang=EN-US>Integrate</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">还可以带一定的参数选项，以控制积分的进行：</SPAN></b></font></P>
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<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>选项参数</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"
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<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>缺省值</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"
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<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>意义</b></font></SPAN></P></TD></TR>
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<TD
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<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><font size="4"><b>PrincipalValue</b></font></SPAN></P></TD>
<TD
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<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><font size="4"><b>False</b></font></SPAN></P></TD>
<TD
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<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>是否求柯西主值</b></font></SPAN></P></TD></TR>
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<TD
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<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><font size="4"><b>GenerateConditions</b></font></SPAN></P></TD>
<TD
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<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><font size="4"><b>True</b></font></SPAN></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"
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<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>结果是否显式地给出条件</b></font></SPAN></P></TD></TR>
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<TD
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<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><font size="4"><b>Assumptions</b></font></SPAN></P></TD>
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<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><font size="4"><b>{
}</b></font></SPAN></P></TD>
<TD
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<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>是否对参数进行假定</b></font></SPAN></P></TD></TR></TBODY></TABLE>
<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>看下面的例子：</b></font></SPAN></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><font size="4"><b>In[1]:=Integrate[x^n, {x, 0, 1}, GenerateConditions ->
False]</b></font></SPAN></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><font size="4"><b>Out[1]<B
style="mso-bidi-font-weight: normal">=</B> <SPAN
style="mso-text-raise: -12.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1036
style="HEIGHT: 30.75pt; WIDTH: 27pt" 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/3.htm84.gif"
v:shapes="_x0000_i1036" width="36" height="41"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1036"
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</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">当设置</font></b></SPAN><b><font size="4"><SPAN
lang=EN-US>GenerateConditions -> False</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">时，</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'">将参数</SPAN><SPAN
lang=EN-US>n</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">作为一般的值对待，并不考虑特殊情况。我们可以使用</SPAN><SPAN
lang=EN-US>Assumptions</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">选项给积分附加一些条件。对上例我们分别假定</SPAN><SPAN
lang=EN-US>n>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>n=1</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">和</SPAN><SPAN
lang=EN-US>n=-1</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">的情况分别计算：</SPAN></font></b></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><font size="4"><b>In[2]:=Integrate[x^n, {x, 0, 1}, Assumptions -> (n >
1)]</b></font></SPAN></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><font size="4"><b>Out[2]= <SPAN
style="mso-text-raise: -12.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1037
style="HEIGHT: 30.75pt; WIDTH: 27pt" 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/3.htm85.gif"
v:shapes="_x0000_i1037" width="36" height="41"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1037"
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</b></font>
</SPAN></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><font size="4"><b>In[3]:=Integrate[x^n, {x, 0, 1}, Assumptions -> (n =
1)]</b></font></SPAN></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN
lang=EN-US>Simplify</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>bass</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>1 is not a well formed assumption.</SPAN></b></font></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN
lang=EN-US>Simplify</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>bass</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>1 is not a well formed assumption.</SPAN></b></font></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><font size="4"><b>Out[3]=<SPAN
style="mso-text-raise: -12.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1038
style="HEIGHT: 30.75pt; WIDTH: 12pt" o:ole="" type="#_x0000_t75"> <V:IMAGEDATA
o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image026.wmz"></V:SHAPE><![endif]--><IMG src="images/3.htm86.gif"
v:shapes="_x0000_i1038" width="16" height="41"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1038"
DrawAspect="Content" ObjectID="_1048959447">
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</b></font>
</SPAN></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><font size="4"><b>In[4]:=Integrate[x^n, {x, 0, 1}, Assumptions -> (n =
-1)]</b></font></SPAN></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN
lang=EN-US>Integrate</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>"idiv"</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><SPAN
style="mso-spacerun: yes"><b><font size="4"> </font></b> </SPAN><b><font size="4">Integral of<SPAN
style="mso-text-raise: -12.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1039
style="HEIGHT: 30.75pt; WIDTH: 12pt" o:ole="" type="#_x0000_t75"> <V:IMAGEDATA
o:title=""
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