第七讲 matlab 的符号计算
DESCRIPTION
第七讲 MATLAB 的符号计算. 所谓符号计算是指在运算时 , 无须事先对变量赋值 , 而将所得到结果以标准的符号形式来表示。 MathWorks 公司以 Maple 的内核作为符号计算引擎( Engine ),依赖 Maple 已有的函数库,开发了实现符号计算的两个工具箱:基本符号工具箱和扩展符号工具箱。. 一、符号计算基础. 一、符号计算基础. (一) 定义符号变量 - PowerPoint PPT PresentationTRANSCRIPT
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MATLAB
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,,MathWorksMapleEngineMaple
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symsymsfindsym
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1sym symsym
x = sym(x)
xx,
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a,b,x,ya,b,x,y
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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
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2 z=x+i*y, , x^2+y^2xyx=sym(x,real);y=sym(y,real);
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z=x+i*y; %conj(z); %expand(z*conj(z)) %ans =x^2+y^2x, x = sym(x,unreal) x
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2symssymssymsyms syms arg1 arg2 argN rg1, arg2,,argN
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f=ax2+bx+ca,b,cx
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f=xn g=sin(at+b)a,b,cxMATLABsyms abntxa,b,cxt fdf/dx gdg/dt
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findsym findsymf,nf n n=i,in
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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
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1+sqr(5*x))/2x
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fxy syms a b c x y % fxy=(a*x^2+b*y^2)/c^2 %fxy
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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)
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1. limitf
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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
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syms x %f=(x*(exp(sin(x))+1)-2*(exp(tan(x))-1))/sin(x)^3 %w=limit(f) %w = -1/2
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2. diffs diff(s,v,n) diffsfindsyms diffsvdiffssymv vs diffsnsnn diffsvndiffsnv vsn
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x = sym('x'); %t = sym('t');diff(sin(x^2)) %ans =2*cos(x^2)*x
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3ints vab)s ints vab)intsfindsymsintsvvs abab
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syms xint(1/(1+x^2)) ans =atan(x)
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4. () f(x)=a0+a1x+a2x2+a3x3++anxnsymsumfsab symsum(s, a,b)
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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
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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)
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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
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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
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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))
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2.
f(x)=sin(x) f(x)=1/cos(x)