📄 第五节 用mathematica进行向量运算和作图.htm
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<title>第五节 用Mathematica进行向量运算和作图</title>
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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>
| <a href="第五节%20用Mathematica进行向量运算和作图.htm">第五节</a>
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<P align=center class=MsoNormal style="text-align: center; line-height: 200%"><font color="#FF0000" size="5"><b><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">第五节</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'">进行向量运算和作图</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'">向量是解决许多数学、物理、力学及工程技术问题的一个有力的工具。微积分中的许多重要概念和原理都有直观的几何解释，将抽象的数学概念和原理与几何的直观有机地结合，不仅可以加深理解，而且启发想象能力和创造能力。几何的方法是现代数学重要的组成部分，向量是空间解析几何的基础。只有掌握了向量及其运算，才能进一步学好空间解析几何。</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'">不仅提供了微积分运算，而且提供丰富的向量运算功能和函数作图功能。本节我们用</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'">作向量运算和进行函数作图。</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 color="#FF0000" size="5">一、<a name="向量表示及运算">向量表示及运算</a></font></b></SPAN></P>
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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>Mathematica</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">中用表表示向量，比如：</SPAN><SPAN
lang=EN-US>a:={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>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>2}</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">表示向量</SPAN><SPAN
lang=EN-US>a=3i+5j+2k</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">。以下给出向量运算的命令格式（</SPAN><SPAN
lang=EN-US>a,b</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">表示向量）：</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'"><font size="4"><b>命令</b></font></SPAN></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'"><font size="4"><b>含义</b></font></SPAN></P></TD></TR>
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<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><font size="4"><b>a+b</b></font></SPAN></P></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'"><b><font size="4">计算向量</font></b></SPAN><b><font size="4"><SPAN
lang=EN-US>a</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">与</SPAN><SPAN
lang=EN-US>b</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">的和</SPAN></font></b></P></TD></TR>
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<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><font size="4"><b>a-b</b></font></SPAN></P></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'"><b><font size="4">计算向量</font></b></SPAN><b><font size="4"><SPAN
lang=EN-US>a</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">与</SPAN><SPAN
lang=EN-US>b</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">的差</SPAN></font></b></P></TD></TR>
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<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><font size="4"><b>a.b</b></font></SPAN></P></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'"><b><font size="4">计算向量</font></b></SPAN><b><font size="4"><SPAN
lang=EN-US>a</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">与</SPAN><SPAN
lang=EN-US>b</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">的点积</SPAN></font></b></P></TD></TR>
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<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><b><font size="4">Det[{{i,j,k}</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>a,b}]</SPAN></font></b></P></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'"><b><font size="4">计算向量</font></b></SPAN><b><font size="4"><SPAN
lang=EN-US>a</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">与</SPAN><SPAN
lang=EN-US>b</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">的叉积</SPAN></font></b></P></TD></TR>
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