MATLAB

,,MathWorksMapleEngineMaple

symsymsfindsym

1sym symsym

x = sym(x)

xx,

1

a,b,x,ya,b,x,y

a=sym(a); %aay =2/bb=sym(b);x=sym(x);y=sym(y); [x,y]=solve(a*x-b*y-1,a*x+b*y-5,x,y) %a,bx,yx =3/ay =2/b

2 z=x+i*y, , x^2+y^2xyx=sym(x,real);y=sym(y,real);

z=x+i*y; %conj(z); %expand(z*conj(z)) %ans =x^2+y^2x, x = sym(x,unreal) x

2symssymssymsyms syms arg1 arg2 argN rg1, arg2,,argN

f=ax2+bx+ca,b,cx

f=xn g=sin(at+b)a,b,cxMATLABsyms abntxa,b,cxt fdf/dx gdg/dt

findsym findsymf,nf n n=i,in

3 f=xn g=sin(at+b)syms a b n t x %f=x^n; %g=sin(a*t+b);findsym(f,1) %f1ans= xf1x

,

1+sqr(5*x))/2x

fxy syms a b c x y % fxy=(a*x^2+b*y^2)/c^2 %fxy

4 fxy=(a*x2+b*y2)/c2 xyxsyms a b c x y %fxy=(a*x^2+b*y^2)/c^2 % diff(fxyx) %fxyxans =2*a*x/c^2diff(fxy y) %fxyy ans =2*b*y/c^2 %fxyxint(fxy x) ans =1/c^2*(1/3*a*x^3+b*y^2*x)

1. limitf

limit(f,x,a)fxxafx limit(f,a)fxfxfxfindsym(f)xalimit(f)fxfxfindsym(f)0a=0limit(f,x,a,'right')f'right'xalimit(f,x,a,'left')f'left'xa

5

syms x %f=(x*(exp(sin(x))+1)-2*(exp(tan(x))-1))/sin(x)^3 %w=limit(f) %w = -1/2

2. diffs diff(s,v,n) diffsfindsyms diffsvdiffssymv vs diffsnsnn diffsvndiffsnv vsn

6

x = sym('x'); %t = sym('t');diff(sin(x^2)) %ans =2*cos(x^2)*x

3ints vab)s ints vab)intsfindsymsintsvvs abab

7

syms xint(1/(1+x^2)) ans =atan(x)

4. () f(x)=a0+a1x+a2x2+a3x3++anxnsymsumfsab symsum(s, a,b)

8:1/12+1/22+1/32+1/42+ syms k symsum(1/k^2,1,Inf) %k1ans =1/6*pi^21/12+1/22+1/32+1/42+ =2/6

1.factorS factor(s)9(x^9-1)syms xfactor(x^9-1)ans =(x-1)*(x^2+x+1)*(x^6+x^3+1)

2.sHorner horner(s)10x^3-6*x^2+11*x-6syms xhorner(x^3-6*x^2+11*x-6)ans =-6+(11+(-6+x)*x)*x

solve(expr1,expr2,...,exprN,var1,var2,...varN) solve(expr1,expr2,...,exprN) expr1,expr2,...,exprNvar1,var2,...varNexpr1,expr2,...,exprN0x^2-3*x-8,x^2-3*x-8=0

11a*x2-b*x-6=0syms a b xsolve(a*x^2-b*x-6) ans = [ 1/2/a*(b+(b^2+24*a)^(1/2))][ 1/2/a*(b-(b^2+24*a)^(1/2))]: x1=1/2/a*(b+(b^2+24*a)^(1/2)) x2=1/2/a*(b-(b^2+24*a)^(1/2))

1

2.

f(x)=sin(x) f(x)=1/cos(x)