📄 第四节 用mathematica解方程和作级数运算.htm
字号:
lang=EN-US><SPAN
style="mso-text-raise: -5.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1028
style="HEIGHT: 17.25pt; WIDTH: 14.25pt" o:ole="" type="#_x0000_t75">
<V:IMAGEDATA o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image003.wmz"></V:SHAPE><![endif]--><IMG src="images/4.htm97.gif"
v:shapes="_x0000_i1028" width="12" height="11"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1028"
DrawAspect="Content" ObjectID="_1048959539">
</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></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=533>
<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">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'">的数值解</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'">近似值</SPAN><SPAN
lang=EN-US>)</SPAN></font></b></P></TD></TR>
<TR>
<TD
style="mso-border-top-alt: solid windowtext .75pt; border-left: 0.75pt solid windowtext; 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=253>
<P class=MsoNormal style="line-height: 200%"><SPAN lang=EN-US><font size="4"><b>NSolve[eqns]</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"
vAlign=top width=533>
<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'">中所有的未知量的数值解</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'">近似值</SPAN><SPAN
lang=EN-US>)</SPAN></font></b></P></TD></TR></TBODY></TABLE>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><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'">的表现形式有以下几种：</SPAN></b></font></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%"><font size="4"><b><SPAN lang=EN-US>{lhs1=
=rhs1</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>lsh2= =rhs2</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></b></font></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><font size="4"><b>{lhs1=
=rhs1&&lsh2= =rhs2&&…}</b></font></SPAN></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN
lang=EN-US>{lhs1</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>lsh2</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>…}= ={rhs1</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>rhs2</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></b></font></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">在</font></b></SPAN><b><font size="4"><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'">中，方程中出现的“</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'">”应写成“</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'">”的形式。例如：</SPAN><SPAN
lang=EN-US>3x^2+5x= =9</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，这条语句将被编译为一个逻辑语句，即判定“</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'">”两端是否相等，上式是判定</SPAN><SPAN
lang=EN-US>3x^2+5x</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">是否等于</SPAN><SPAN
lang=EN-US>9</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，相等返回</SPAN><SPAN
lang=EN-US>True</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，否则返回</SPAN><SPAN
lang=EN-US>False</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'">”是一个赋值语句，</SPAN><SPAN
lang=EN-US>x=9</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">表示把</SPAN><SPAN
lang=EN-US>9</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">赋给</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'">，在此以下的语句中，</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'">代表数字</SPAN><SPAN
lang=EN-US>9</SPAN><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="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'">例</SPAN><SPAN
lang=EN-US>1</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">求解下列方程</SPAN><SPAN
lang=EN-US>:</SPAN></b></font></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><font size="4"><b><SPAN
style="mso-text-raise: -73.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1029
style="HEIGHT: 152.25pt; WIDTH: 264.75pt" o:ole=""
type="#_x0000_t75"><V:IMAGEDATA o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image007.wmz"></V:SHAPE><![endif]--><IMG src="images/4.htm98.gif"
v:shapes="_x0000_i1029" width="353" height="203"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1029"
DrawAspect="Content" ObjectID="_1048959540">
</o:OLEObject>
</xml><![endif]-->
</b></font>
</SPAN></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'"><font size="4"><b>解：</b></font></SPAN></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>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>In[1]:=Solve[x^2 + 9x - 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[1]=</SPAN><SPAN lang=EN-US style="mso-text-raise: -12.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1030
style="HEIGHT: 30.75pt; WIDTH: 215.25pt" o:ole="" type="#_x0000_t75">
<V:IMAGEDATA o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image009.wmz"></V:SHAPE><![endif]--><IMG src="images/4.htm99.gif"
v:shapes="_x0000_i1030" width="280" height="34"></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_i1030"
DrawAspect="Content" ObjectID="_1048959541">
</o:OLEObject>
</xml><![endif]-->
</SPAN></b></font></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN
lang=EN-US>In[2]:=NSolve[x^2 + 9x - 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[2]={{x
-> -9.21699}</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 -> 0.216991}}</SPAN></b></font></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'"><font size="4"><b>仔细比较输出中显式解（表达式）和数值解有何不同。</b></font></SPAN></P>
<P class=MsoNormal style="line-height: 200%"><font size="4"><b><SPAN
⌨️ 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 + -