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<P class=MsoNormal style="TEXT-ALIGN: center" align=center><B
style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 22pt; COLOR: black; mso-bidi-font-size: 10.0pt">MATLAB</SPAN></B><B
style="mso-bidi-font-weight: normal"><SPAN
style="FONT-SIZE: 22pt; COLOR: black; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">入门教程</SPAN></B><B
style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 22pt; COLOR: black; mso-bidi-font-size: 10.0pt"><O:P></O:P></SPAN></B></P>
<P class=MsoNormal style="TEXT-ALIGN: center" align=center><B
style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 22pt; COLOR: black; mso-bidi-font-size: 10.0pt"><![if !supportEmptyParas]><![endif]> <O:P></O:P></SPAN></B><B
style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 16pt; COLOR: blue; mso-bidi-font-size: 10.0pt">2</SPAN></B><B
style="mso-bidi-font-weight: normal"><SPAN
style="FONT-SIZE: 16pt; COLOR: blue; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">．数值分析</SPAN></B><B
style="mso-bidi-font-weight: normal"><SPAN
style="FONT-SIZE: 16pt; COLOR: blue; mso-bidi-font-size: 10.0pt">
</SPAN></B></P>
<P class=MsoNormal><B style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 14pt; mso-bidi-font-size: 10.0pt">2</SPAN></B><B
style="mso-bidi-font-weight: normal"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">．</SPAN></B><B
style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 14pt; mso-bidi-font-size: 10.0pt">1</SPAN></B><B
style="mso-bidi-font-weight: normal"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">微分</SPAN></B><B
style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 14pt; mso-bidi-font-size: 10.0pt"><SPAN
style="mso-spacerun: yes"> </SPAN><O:P></O:P></SPAN></B></P>
<P class=MsoNormal><SPAN lang=EN-US>diff</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">函数用以演算一函数的微分项，相关的函数语法有下列</SPAN><SPAN
lang=EN-US>4</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">个：</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>diff(f) </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">传回</SPAN><SPAN
lang=EN-US>f</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">对预设独立变数的一次微分值</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>diff(f,'t') </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">传回</SPAN><SPAN
lang=EN-US>f</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">对独立变数</SPAN><SPAN
lang=EN-US>t</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">的一次微分值</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>diff(f,n) </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">传回</SPAN><SPAN
lang=EN-US>f</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">对预设独立变数的</SPAN><SPAN
lang=EN-US>n</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">次微分值</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>diff(f,'t',n) </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">传回</SPAN><SPAN
lang=EN-US>f</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">对独立变数</SPAN><SPAN
lang=EN-US>t</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">的</SPAN><SPAN
lang=EN-US>n</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">次微分值</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US><SPAN
style="mso-spacerun: yes"> </SPAN></SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">数值微分函数也是用</SPAN><SPAN
lang=EN-US>diff</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，因此这个函数是靠输入的引数决定是以数值或是符号微分，如果引数为向量则执行数值微分，如果引数为符号表示式则执行符号微分。</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US><SPAN
style="mso-spacerun: yes"> </SPAN></SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">先定义下列三个方程式，接著再演算其微分项：</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>>>S1 = '6*x^3-4*x^2+b*x-5';<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>>>S2 = 'sin(a)';<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>>>S3 = '(1 - t^3)/(1 + t^4)';<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>>>diff(S1)<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>ans=18*x^2-8*x+b<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>>>diff(S1,2)<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>ans= 36*x-8<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>>>diff(S1,'b')<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>ans= x<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>>>diff(S2)<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>ans=<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>cos(a)<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>>>diff(S3)<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN
lang=EN-US>ans=-3*t^2/(1+t^4)-4*(1-t^3)/(1+t^4)^2*t^3<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>>>simplify(diff(S3))<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>ans= t^2*(-3+t^4-4*t)/(1+t^4)^2<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><B style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 14pt; mso-bidi-font-size: 10.0pt">2</SPAN></B><B
style="mso-bidi-font-weight: normal"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">．</SPAN></B><B
style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 14pt; mso-bidi-font-size: 10.0pt">2</SPAN></B><B
style="mso-bidi-font-weight: normal"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">积分</SPAN></B><B
style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 14pt; mso-bidi-font-size: 10.0pt"><SPAN
style="mso-spacerun: yes"> </SPAN><O:P></O:P></SPAN></B></P>
<P class=MsoNormal><SPAN lang=EN-US><SPAN
style="mso-spacerun: yes"> </SPAN>int</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">函数用以演算一函数的积分项，</SPAN>
<SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">这个函数要找出一符号式</SPAN><SPAN
lang=EN-US> F </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">使得</SPAN><SPAN
lang=EN-US>diff(F)=f</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">。如果积</SPAN><SPAN
lang=EN-US> </SPAN></P>
<P class=MsoNormal><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">分式的解析式</SPAN><SPAN
lang=EN-US> (analytical form, closed form) </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">不存在的话或是</SPAN><SPAN
lang=EN-US>MATLAB</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">无法找到，则</SPAN><SPAN
lang=EN-US>int </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">传回原输入的符号式。相关的函数语法有下列</SPAN><SPAN
lang=EN-US> 4</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">个：</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>int(f) </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">传回</SPAN><SPAN
lang=EN-US>f</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">对预设独立变数的积分值</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>int(f,'t') </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">传回</SPAN><SPAN
lang=EN-US>f</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">对独立变数</SPAN><SPAN
lang=EN-US>t</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">的积分值</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>int(f,a,b) </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">传回</SPAN><SPAN
lang=EN-US>f</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">对预设独立变数的积分值，积分区间为</SPAN><SPAN
lang=EN-US>[a,b]</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，</SPAN><SPAN
lang=EN-US>a</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">和</SPAN><SPAN
lang=EN-US>b</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">为数值式</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>int(f,'t',a,b) </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">传回</SPAN><SPAN
lang=EN-US>f</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">对独立变数</SPAN><SPAN
lang=EN-US>t</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">的积分值，积分区间为</SPAN><SPAN
lang=EN-US>[a,b]</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，</SPAN><SPAN
lang=EN-US>a</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">和</SPAN><SPAN
lang=EN-US>b</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">为数值式</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>int(f,'m','n') </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">传回</SPAN><SPAN
lang=EN-US>f</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">对预设变数的积分值，积分区间为</SPAN><SPAN
lang=EN-US>[m,n]</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，</SPAN><SPAN
lang=EN-US>m</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">和</SPAN><SPAN
lang=EN-US>n</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">为符号式</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">我们示范几个例子：</SPAN><SPAN
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