matlab符号计算.doc

第四章 符号计算4.1符号变量和符号表达式例ex4_1：1）syms a b c x; %定义符号变量f=sym(a*x2+b*x+c); %定义符号表达式2）syms a b c x; %定义符号变量f1=sym(a*x2+b*x+c); %定义符号表达式3）syms a b c x; %定义符号变量f2=a*x2+b*x+c; %定义符号表达式例ex4_2：syms x y z;r=sqrt(x2+y2+z2);%只定义符号变量,不定义符号表达式f=sin(x*y)/(x*y);4.2符号矩阵例ex4_3：a1=1/3,pi/7,sqrt(5),pi+sqrt(5);%a1为数值常数矩阵a2=sym(1/3,pi/7,sqrt(5),pi+sqrt(5);%a2为符号矩阵syms x;a3=2/3,(x2+3)/(2*x-1),4/x2;%a3为符号矩阵4.3因式分解、展开和简化例ex4_4：syms a x;f1=x4-5*x3+5*x2+5*x-6factor(f1) %对f1因式分解：例ex4_5：syms x;f=(1/x3+6/x2+12/x+8)(1/3)g1=simple(f)%化简：g2=simple(g1)g3=simple(g2)例ex4_6：syms x y;s=sym(sin(x+y)/cos(2*x)se=expand(s)%展开：4.4级数求和例ex4_7：syms x k;s=symsum(1/k2,k,1,inf)%1/k2在k=1到无穷项求和s1=symsum(xk,k,0,50)4.5极限例ex4_8：syms h x;f=sym(cos(x+h)-cos(x)/h)dc=limit(f,h,0)%求f在h趋于0 时的极限例ex4_9：sym x;f=sym(1/x)dc=limit(f,x,0)dcl=limit(f,x,0,left)%左极限dcr=limit(f,x,0,right)%右极限4.6微分例ex4_10：syms x a;f=sin(a*x)df=diff(f)%f对x微分dfa=diff(f,a)%f对a微分df2=diff(f,2)%f对x二阶微分dfa2=diff(f,a,2)4.6积分例ex4_11：f=sym(sin(s+2*x)fx=int(f)%以x为积分变量fs=int(f,s)%以s为积分变量fx1=int(f,pi/2,pi)%以x为积分变量,上下限为、/2fs1=int(f,s,pi/2,pi)fxmn=int(f,m,n)4.7代数方程求解例ex4_12：sym x;s=solve(x+2)x=2,x)例ex4_13：clear all;a=sym(1,1/2,1/2,-1;1,1,-1,1;1,-1/4,-1,1;-8,-1,1,1)b=sym(0;10;0;1)x=ab%线形方程组求解例ex4_14：求x2-ay=0,bx=2的解clear;syms x y a b;x,y=solve(x2-a*y,b*x-2,x,y)4.8微分方程求解例ex5_15：求dx/dt=y,dy/dt=-x的通解clear all;x,y=dsolve(Dx=y,Dy=-x)disp(blanks(12),x,blanks(21),y)disp(x,y)例ex4_16：求dx/dt=3x+4y,dy/dt=-4x+3y的解，初始条件x(0)=0,y(0)=1clear all;x,y=dsolve(Dx=3*x+4*y,Dy=-4*x+3*y,x(0)=0,y(0)=1)disp(x;y);4.9符号函数的图形例ex5_17：clear all;x,y=dsolve