📄 第四节 用mathematica解方程和作级数运算.htm
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<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"><a href="index.htm">主目录</a></span><span style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">
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| <a href="第四节%20用Mathematica解方程和作级数运算.htm">第四节</a>
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style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">第四节</SPAN>
<SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">用</SPAN><SPAN
lang=EN-US>Mathematica</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">解方程和作级数运算</SPAN></font></b></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'">方程求解是高等数学中的一个重要内容，同时也是软件</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'">的一个重要方面。方程求解是十分复杂的，并非对所有的方程</SPAN><SPAN
lang=EN-US>Mathematica</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">都能解出，要想给出方程的精确的代数表达时就更难了。对于我们常见的方程（组）</SPAN><SPAN
lang=EN-US>Mathematica</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">都能给出其精确的表达式的解。对于广大的科技工作者来说，数值解的求解往往也是一个非常重要的要求。以下将讨论一般方程（组）和常微分方程的解法。</SPAN></b></font></P>
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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">一、<a name="一元方程和联立方程组">一元方程和联立方程组</a></font></b></SPAN></P>
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lang=EN-US><b><font size="4">Mathematica</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'">在编制精确求解方程函数的同时，也注意到了方程的数值解。一元方程和联立方程组的求解析解都是通过函数</SPAN><SPAN
lang=EN-US><font color="#FF0000">Solve</font></SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">来实现的，数值解可通过</SPAN><SPAN
lang=EN-US><font color="#FF0000">NSolve</font></SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">来求。对于不高于四次的多项式方程，</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'">总能给出方程的显式解。以下给出这两个函数的格式：</SPAN></font></b></P>
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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>
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<P class=MsoNormal style="line-height: 200%"><SPAN lang=EN-US><b><font size="4">Solve[eqns</font></b></SPAN><b><font size="4"><SPAN
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lang=EN-US>…}]</SPAN></font></b></P></TD>
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style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><b><font size="4">以</font></b></SPAN><b><font size="4"><SPAN
lang=EN-US>xi</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">为未知量求解方程</SPAN><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'">的解析解（准确值）</SPAN></font></b></P></TD></TR>
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<P class=MsoNormal style="line-height: 200%"><SPAN lang=EN-US><font size="4"><b>Solve[eqns]</b></font></SPAN></P></TD>
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<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'">中所有的未知量的解析解（准确值）</SPAN></font></b></P></TD></TR>
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<P align=left class=MsoNormal style="line-height: 200%"><SPAN lang=EN-US><b><font size="4">NSolve[eqns</font></b></SPAN><b><font size="4"><SPAN
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