Matlab教程Ch4(高等数学).ppt

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1、1数值运算在运算前必须先对变量赋值，再参加运算。符号运算不需要对变量赋值就可运算，运算结果以标准的符号形式表达。MATLAB符号运算2>>x=sym('x');y=sym(y);z=sym(z);%or>>symsxyz>>f1=sym(‘ax^2+bx+c’)或者>>clear>>symsabcx>>f2=a*x^2+b*x+c3>>f=sym('x^2+2*x+y');>>x=2*pi;y=1;>>f1=eval(f)%或>>f2=subs(f)%或>>subs(f,{x,y},{2*pi,1})>>subs

2、(f,'x','s')>>f3=subs(f,'x','3'),vpa(f3)>>f4=subs(f,x,3)4collect函数—合并同类项>>clear>>symsxy>>f=(x-y)^3;>>collect(f,y)fcollect(f)(x-1)*(x-2)*(x-3)x^3-6*x^2+11*x-6x*(x*(x-6)+11)-6x^3-6*x^2+11*x-6(1+x)*t+x*t2*x*t+t(x-y)^3x^3-3*x^2*y+3*y^2*x-y^35expand函数—将乘积展开为和式>>f=sym(

3、'cos(x+y)');>>expand(f)fexpand(f)a*(x+y)a*x+a*y(x-1)*(x-2)*(x-3)x^3-6*x^2+11*x-6x*(x*(x-6)+11)-6x^3-6*x^2+11*x-6exp(a+b)exp(a)*exp(b)cos(x+y)cos(x)*cos(y)-sin(x)*sin(y)cos(3*acos(x))4*x^3-3*x6horner函数—把多项式转换为嵌套表示形式fhorner(f)x^3-6*x^2+11*x-6-6+(11+(-6+x)*x)*x1.1+

4、2.2*x+3.3*x^211/10+(11/5+33/10*x)*x7factor函数—把多项式转换为乘积形式>>symsx;>>n=(1:9)';>>p=x.^n+1;>>f=factor(p);>>[p,f]ffactor(f)x^3-6*x^2+11*x-6(x-1)*(x-2)*(x-3)x^3-6*x^2+11*x-5x^3-6*x^2+11*x-5x^6+1(x^2+1)*(x^4-x^2+1)8Pretty函数—手写>>clear>>symsx>>f=x^3-6*x^2+11*x-6;>>g=(x-1)

5、*(x-2)*(x-3);>>h=-6+(11+(-6+x)*x)*x;>>pretty(f),pretty(g),pretty(h)32x-6x+11x-6(x-1)(x-2)(x-3)-6+(11+(-6+x)x)x9simplify函数—化简fsimplify(f)x*(x*(x-6)+11)-6x^3-6*x^2+11*x-6(1-x^2)/(1-x)x+1(1/a^3+6/a^2+12/a+8)^(1/3)((2*a+1)^3/a^3)^(1/3)symsxypositive;log(x*y)log(x)+l

6、og(y)exp(x)*exp(y)exp(x+y)cos(x)^2+sin(x)^2110simple函数—列出化简步骤>>f=sym('cos(x)^2+sin(x)^2')>>simplify(f)>>simple(f)>>f1=simple(f)fsimplify(f)simple(f)(1/a^3+6/a^2+12/a+8)^(1/3)((2*a+1)^3/a^3)^(1/3)(2*a+1)/asymsxypositive;log(x*y)log(x)+log(y)log(x*y)有时simple函数比sim

7、plify的结果更简化！>>f=(1/a^3+6/a^2+12/a+8)^(1/3);>>Simple_f=simple(f)>>Simple_Simple_f=simple(Simple_f)Simple_Simple_f=2+1/a%或>>Simple_Simple_f=simple(simple(f))Simple_Simple_f=2+1/a有时运用2次simple函数得到的结果更好！11>>symsxy>>f=1/(1+x);>>g=cos(y);>>compose(f,g)运行结果：ans=1/(cos(y

8、)+1)compose函数—复合函数12>>symsx>>y=1/cos(x);>>g=finverse(y)运行结果：g=acos(1/x)finverse函数—反函数13第4章高等数学中的Matlab命令格式五种:符号变量说明:symsxythalimit(f,x,a)limit(f,a)默认变量x或唯一符号变量limit(f