📄 sxsy05_211.mht
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style=3D'mso-bidi-font-weight:normal'><span lang=3DEN-US style=3D'font-size=
:12.0pt'><o:p></o:p></span></b></p>
<p class=3DMsoNormal style=3D'text-indent:21.0pt;mso-char-indent-count:2.0'=
><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>本实验介绍数学=
软件</span><span
class=3DSpellE><span lang=3DEN-US>Mathematica</span></span><span style=3D'f=
ont-family:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>的程序设计功能Ӎ=
0;</span></p>
<p class=3DMsoNormal style=3D'text-indent:21.0pt;line-height:125%;vertical-=
align:
top'><b style=3D'mso-bidi-font-weight:normal'><span style=3D'font-family:Si=
mSun;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Ro=
man"'>（一）自定义函数</spa=
n><span
lang=3DEN-US><o:p></o:p></span></b></p>
<p class=3DMsoNormal style=3D'text-indent:21.0pt;line-height:125%;vertical-=
align:
top'><span style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Rom=
an";
mso-hansi-font-family:"Times New Roman"'>在</span><span class=3DSpell=
E><span
lang=3DEN-US>Mathematica</span></span><span style=3D'font-family:SimSun;mso=
-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>中，=
除了系统定义的常用=
0989;数以外，当我们需ව=
1;使用自己的函数来完&=
#25104;特定的任务时，可=
197;使用自定义函数的方=
;法来定义我们自己所&#=
38656;要的函数。</span></p>
<p class=3DMsoNormal style=3D'text-indent:21.0pt;line-height:125%;vertical-=
align:
top'><span style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Rom=
an";
mso-hansi-font-family:"Times New Roman"'>自定义的&#=
26041;法是：</span></p>
<p class=3DMsoNormal style=3D'text-indent:42.0pt;line-height:125%;vertical-=
align:
top'><span lang=3DEN-US>f[x_]:=3D</span><span style=3D'font-family:SimSun;m=
so-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>包含=
</span><span
lang=3DEN-US>x</span><span style=3D'font-family:SimSun;mso-ascii-font-famil=
y:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>的表达式</=
span></p>
<p class=3DMsoNormal style=3D'text-indent:42.0pt;line-height:125%;vertical-=
align:
top'><span lang=3DEN-US>f[x_ , y_]:=3D</span><span style=3D'font-family:Sim=
Sun;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Ro=
man"'>包含</span><span
lang=3DEN-US>x</span><span style=3D'font-family:SimSun;mso-ascii-font-famil=
y:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>，</span><span lang=3DEN-US>=
y</span><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>的表达式</span></p>
<p class=3DMsoNormal style=3D'text-indent:21.0pt;line-height:125%;vertical-=
align:
top'><span style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Rom=
an";
mso-hansi-font-family:"Times New Roman"'>这里</span><span
lang=3DEN-US>x_</span><span style=3D'font-family:SimSun;mso-ascii-font-fami=
ly:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>可以为实&#=
25968;、向量或矩阵。</span></p>
<p class=3DMsoNormal style=3D'text-indent:21.0pt;line-height:125%;vertical-=
align:
top'><span style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Rom=
an";
mso-hansi-font-family:"Times New Roman"'>系统还允&#=
35768;两个不同的函数取İ=
56;同的函数名。</span></p>
<p class=3DMsoNormal style=3D'text-indent:21.0pt;line-height:125%;vertical-=
align:
top'><span style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Rom=
an";
mso-hansi-font-family:"Times New Roman"'>例</span><span lang=3DEN-US>=
1</span><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>：</span><span class=3DGramE><span lang=3DEN-US>g[=
</span></span><span
lang=3DEN-US>x_]:=3Dx^2+Sin[x]</span></p>
<p class=3DMsoNormal style=3D'text-indent:53.25pt;line-height:125%;vertical=
-align:
top'><span class=3DGramE><span lang=3DEN-US>g[</span></span><span lang=3DEN=
-US>x_ ,
y_]:=3D<span class=3DSpellE>x+y</span></span></p>
<p class=3DMsoNormal style=3D'text-indent:21.0pt;mso-char-indent-count:2.0;
line-height:125%;vertical-align:top'><span style=3D'font-family:SimSun;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Ro=
man"'>这时，系统同时接Ö=
63;了这两个同名的函数=
，并且会根据情况自=
1160;调用相应的表达式Ӎ=
0;但如果我们接着定义<=
/span><span
lang=3DEN-US>g[x_]:=3DLog[x]</span><span style=3D'font-family:SimSun;mso-as=
cii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>，则=
</span><span
lang=3DEN-US>g[x_]</span><span style=3D'font-family:SimSun;mso-ascii-font-f=
amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>的定=
义就被改变了，而</span><span
lang=3DEN-US>g[x_ , y_]</span><span style=3D'font-family:SimSun;mso-ascii-f=
ont-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>依然=
存在。</span></p>
<p class=3DMsoNormal style=3D'text-indent:21.0pt;mso-char-indent-count:2.0;
line-height:125%;vertical-align:top'><span style=3D'font-family:SimSun;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Ro=
man"'>要清除</span><span
lang=3DEN-US>g</span><span style=3D'font-family:SimSun;mso-ascii-font-famil=
y:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>的全部定&#=
20041;，用</span><span
lang=3DEN-US>Clear[g]</span><span style=3D'font-family:SimSun;mso-ascii-fon=
t-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>。而=
如果仅仅希望清除</span><span
lang=3DEN-US>g[x_]</span><span style=3D'font-family:SimSun;mso-ascii-font-f=
amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>的定=
义，则用</span></p>
<p class=3DMsoNormal style=3D'text-indent:21.0pt;mso-char-indent-count:2.0;
line-height:125%;vertical-align:top'><span lang=3DEN-US><span
style=3D'mso-spacerun:yes'> </span><span
class=3DGramE>g[</span>x_]:=3D<b style=3D'mso-bidi-font-weight:normal'>.</b=
></span></p>
<p class=3DMsoNormal style=3D'line-height:125%;vertical-align:top'><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>来完成。</span></p>
<p class=3DMsoNormal style=3D'text-indent:21.75pt;line-height:125%;vertical=
-align:
top'><span style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Rom=
an";
mso-hansi-font-family:"Times New Roman"'>自定义函&#=
25968;的立即赋值和延迟ũ=
71;值：</span></p>
<p class=3DMsoNormal style=3D'text-indent:21.75pt;line-height:125%;vertical=
-align:
top'><span style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Rom=
an";
mso-hansi-font-family:"Times New Roman"'>在</span><span class=3DSpell=
E><span
lang=3DEN-US>Mathematica</span></span><span style=3D'font-family:SimSun;mso=
-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>中，=
定义函数时除了用“</sp=
an><span
lang=3DEN-US>:=3D</span><span style=3D'font-family:SimSun;mso-ascii-font-fa=
mily:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>”外，也=
1487;以用“</span><span
lang=3DEN-US>=3D</span><span style=3D'font-family:SimSun;mso-ascii-font-fam=
ily:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>”来定义=
5292;但二者的意义是不ࡧ=
6;的，我们来看</span><span
lang=3DEN-US>f[x_]:=3D2x</span><span style=3D'font-family:SimSun;mso-ascii-=
font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>和</span><=
span
lang=3DEN-US>g[x_]=3D2x</span><span style=3D'font-family:SimSun;mso-ascii-f=
ont-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>，如=
果</span><span
lang=3DEN-US>x</span><span style=3D'font-family:SimSun;mso-ascii-font-famil=
y:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>没有被定&#=
20041;，则它们二者没有É=
60;么差异，但如果在定=
义函数之前，已经定=
0041;了</span><span
lang=3DEN-US>x=3D2</span><span style=3D'font-family:SimSun;mso-ascii-font-f=
amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>，则=
我们将会发现二者有=
4456;大的差异。我们将߳=
1;用“</span><span
lang=3DEN-US>=3D</span><span style=3D'font-family:SimSun;mso-ascii-font-fam=
ily:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>”定义的=
1216;为立即赋值函数，๢=
5;种函数在定义时赋值&=
#21495;右边的表达式立即"=
987;求值，如果此时右边=
;的变量已经有值，则&#=
35843;用此函数时无法替þ=
42;；二用“</span><span
lang=3DEN-US>:=3D</span><span style=3D'font-family:SimSun;mso-ascii-font-fa=
mily:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>”定义的=
0989;数称为延迟赋值函ਤ=
8;，系统记录的只是一&=
#20010;规则，求值是在调=
992;时才进行的。严格地=
;讲，这才是真正意义&#=
30340;函数。但</span><span
class=3DSpellE><span lang=3DEN-US>Mathematica</span></span><span style=3D'f=
ont-family:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>为了某些需要，ߖ=
3;允许用“</span><span
lang=3DEN-US>=3D</span><span style=3D'font-family:SimSun;mso-ascii-font-fam=
ily:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>”来定义=
0989;数，例如在利用</span><span
lang=3DEN-US>Plot</span><span class=3DGramE><span style=3D'font-family:SimS=
un;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Ro=
man"'>作出</span></span><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>含有计算命令函=
数的图形时，就有这=
6679;的需要。</span></p>
<p class=3DMsoNormal style=3D'text-indent:21.75pt;line-height:125%;vertical=
-align:
top'><span style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Rom=
an";
mso-hansi-font-family:"Times New Roman"'>例</span><span lang=3DEN-US>=
2</span><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>：比较：</span><span lang=3DEN-U=
S>fun[x_]=3DD[Sin[x]^2,x]+Integrate[4x^3,x];Plot[fun[x],{x,-1,1}]</span></p>
<p class=3DMsoNormal style=3D'text-indent:21.75pt;line-height:125%;vertical=
-align:
top'><span style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Rom=
an";
mso-hansi-font-family:"Times New Roman"'>和</span> <span lang=3DEN-US=
>fun[x_]:=3DD[Sin[x]^2,x]+Integrate[4x^3,x];
Plot[fun[x],{x,-1,1}]</span><span style=3D'font-family:SimSun;mso-ascii-fon=
t-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>的差=
异。</span></p>
<p class=3DMsoNormal style=3D'line-height:125%;vertical-align:top'><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>解：前者在运行=
时没有问题，但后者=
0001;于调用时没有具体௚=
0;值而无法进行计算，&=
#20294;也不是一定要用第=
968;<span
class=3DGramE>钟方法</span>来定义࠲=
9;数，其实这时可采用&=
#23558;</span><span
lang=3DEN-US>Plot</span><span style=3D'font-family:SimSun;mso-ascii-font-fa=
mily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>语句=
中的</span><span
lang=3DEN-US>fun[x]</span><span style=3D'font-family:SimSun;mso-ascii-font-=
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