Matlab學(xué)習(xí)與實驗教程-第8章 MATLAB符號計算

1、第8章 MATLAB符號計算例8-1 極限I： syms a m x; f=(x*(exp(sin(x)+1)-2*(exp(tan(x)-1)/ (x+a); limit,x,a) ans =(a*(exp(sin (a) + 1) - 2*exp(sin(a)/cos(a) + 2)/(2*a) 極限2： syms x t; limit(l+2*t/x)A(3*x),x,inf) ans = exp(6*t) 極限3： syms x; f=x*(sqrt(xA2+l)-x); limit(fzx,inf,left) ans = 1/2 極限4：syms x; f=(sqrt(x)-sqrt

2、(2)-sqrt(x-2)/sqrt(x*x-4); limit(f,x,2,right) ans = -1/2例8-2求以下函數(shù)的導(dǎo)數(shù)。 syms x y z a t; f=exp(-x)+x; diff (f)*求(1。未指定求導(dǎo)變量和階數(shù)，按默認規(guī)那么處理ans =- exp(-x) f=cos(x*x); diff (f,x,2)告求(2)。求f對x的二階導(dǎo)數(shù)ans = -2*sin(xA2) - 4*xA2*cos(xA2) diff (fzx,3)會求(2)。求f對x的三階導(dǎo)數(shù)ans = 8*xA3*sin(xA2) - 12*x*cos(xA2) fl=a*cos(t);f2=b

3、*sin(t); diff(f2)/diff(fl)告求3。按參數(shù)方程求導(dǎo)公式求y對x的導(dǎo)數(shù)ans =(b*cos(t)/(a*sin(t) (diff(fl)*diff(f2,2)-diff(fl,2)*diff(f2)/(diff(fl)A3 金求(3)。求 y對 x 的二階導(dǎo)數(shù)ans =(a*b*cos(t)2 + a*b*sin(t)2)/(aA3*sin(t)A3) f=x+l/yA2; diff(fzx) ans = 1 diff (fzy) ans = -2/yA3 例8-3 x=sym(* x); f=l/(l+xA2); int(f) ans = atan(x) syms a

4、lpha t int(exp(t),exp(alpha*t) ans =exp(t)z exp(alpha*t)/alpha f=sqrt(1/(1+x); int(fz0z2) ans =2*3A(l/2) - 2 int(4*x*tzt/2,sin(x) ans =2*x*(cos(x)A2 + 3)例8-4 syms n; s=symsum(l/nA2,l,inf)的求（4）。z對x的偏導(dǎo)數(shù)務(wù)求（4）。z對y的偏導(dǎo)數(shù)務(wù)求不定枳分（1）3求（2）務(wù)求定積分（3）告求定積分（4）名求（1）pi-2/6 y=symsum(l/(2*n-l) z lf 10)考求(2)y =31037876/1

5、4549535 eval(y)ans =2.1333例8-5 syms x; fl=(l+x+x2)/ (l-x+xA2);%轉(zhuǎn)換為數(shù)值 taylor (fl)名求(1)ans =-2*xA5 - 2*xA4 + 2*xA2 + 2*x + 1 f2=log(x); taylor (f2,xz lz Order,6)先求(2)。展開到x-l的5次底時應(yīng)選擇n=6 ans =x - (x - 1)A2/2 + (x - 1)A3/3 - (x - 1)A4/4 + (x - 1)5/5 - 1例8-6 syms x y z a x=solve (1/ (x+2) +a=l/ (x-2), x)名

6、解方程(1)x =(2*(a*(a + l)A(l/2)/a(2* (a*(a + l)A(l/2)/a syms x y z (x, y, z =solve (x+2*y-z=27,x+z=3,xA2+3*yA2=12, x, y, z) %解方程(2) x =(627A(1/2)*li)/4 + 45/445/4 - (627A(l/2)*li)/4 y =15/4 - (627A(l/2)*li)/4 (627A(1/2)*li)/4 + 15/4 z =(627A(l/2)*li)/4 - 33/4(627A(l/2)*li)/4 - 33/4例8-7 y=dsolve ( Dy= (tA2+yA2) /tA2/2 , 11 )會解方程(1)y =tt* (1/(C5 + log(t)/2) - 1) y=dsolve ( Dy=2*x*yz2 , 1 y (0) =1, x )會解方程(2)y =-1/