第八讲MATLAB符号运算

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,第八讲 MATLAB符号运算,9/13/2024,9/13/2024,1,第八讲 MATLAB符号运算,8.1,设置符号变量,8.2 微分积分运算,8.3 方程求解,8.4 线性代数运算,8.5 其它命令,9/13/2024,2,8.1,设置符号变量,1.设置符号变量（sym, syms）,S = sym(A),x = sym(x),x = sym(x,real),x = sym(x,unreal),syms arg1 arg2 .,syms arg1 arg2 . real,syms arg1 arg2 . unreal,9/13/2024,3,8.2 微分积分运算,2.1微分,diff(S,v) （s对变量v求偏导）,diff(S,n) （对s求n次导）,diff(S,v,n)（s对变量 v 求n 次偏导）,9/13/2024,4,8.2 微分积分运算,2.2积分,R = int(S),R = int(S,v),R = int(S,a,b),R = int(S,v,a,b),例如：,int(-2*x/(1+x2)2),ans=,1/(1+x2),9/13/2024,5,8.2 微分积分运算, int(exp(-x2),ans =,1/2*pi(1/2)*erf(x), int(exp(-x2),0,inf),ans =,1/2*pi(1/2),9/13/2024,6,8.2 微分积分运算,int(x/(1+z2),z),ans=,atan(z)*x,int(x*log(1+x),0,1),ans=,1/4,int(2*x, sin(t), 1),ans=,1-sin(t)2,9/13/2024,7,8.2 微分积分运算,int(exp(t),exp(alpha*t),ans=,exp(t), 1/alpha*exp(alpha*t),2.3.极限,limit(F,x,a),limit(F,a)（x-a时F的极限）,limit(F) （x-0时F的极限),limit(F,x,a,right),limit(F,x,a,left),9/13/2024,8,8.2 微分积分运算,例如：,syms x a t h;,limit(sin(x)/x) = 1,limit(1/x,x,0,right) = inf,limit(1/x,x,0,left) = -inf,limit(sin(x+h)-sin(x)/h,h,0) = cos(x),9/13/2024,9,8.2 微分积分运算,v = (1 + a/x)x, exp(-x);,limit(v,x,inf,left) = exp(a), 0,2.4.级数和,symsum(s,t,a,b) s中t从a到b求和。, symsum(x2,x,1,n),ans =,1/3*(n+1)3-1/2*(n+1)2+1/6*n+1/6,9/13/2024,10,8.3 方程求解,3.解方程,3.1代数方程（solve）,g = solve(eq),g = solve(eq,var),g = solve(eq1,eq2,.,eqn),g = solve(eq1,eq2,.,eqn,var1,var2,.,varn),9/13/2024,11,8.3 方程求解,如： solve(a*x2 + b*x + c),ans=, 1/2/a*(-b+(b2-4*a*c)(1/2),1/2/a*(-b-(b2-4*a*c)(1/2),solve(a*x2 + b*x + c,b),ans=,-(a*x2+c)/x,solve(x + y = 1,x - 11*y = 5),y = -1/3, x = 4/3,9/13/2024,12,8.3 方程求解,A = solve(a*u2 + v2, u - v = 1, a2 - 5*a + 6),A =,a: 1x4 sym,u: 1x4 sym,v: 1x4 sym,这里A.a =, 2, 2, 3, 3,9/13/2024,13,8.3 方程求解,A.u =, 1/3+1/3*i*2(1/2), 1/3-1/3*i*2(1/2),1/4+1/4*i*3(1/2), 1/4-1/4*i*3(1/2),A.v =, -2/3+1/3*i*2(1/2), -2/3-1/3*i*2(1/2),-3/4+1/4*i*3(1/2), -3/4-1/4*i*3(1/2),9/13/2024,14,8.3 方程求解,3.2微分方程（dsolve）,r = dsolve(eq1,eq2,., cond1,cond2,., v),r = dsolve(eq1,eq2,.,cond1,cond2,.,v),如：,dsolve(Dy = a*y),ans=,exp(a*t)*C1,9/13/2024,15,8.3 方程求解,dsolve(Df = f + sin(t),ans=,-1/2*cos(t)-1/2*sin(t)+exp(t)*C1,dsolve(Dy)2 + y2 = 1,s),ans=,-sin(-s+C1),dsolve(Dy = a*y, y(0) = b),ans=,exp(a*t)*b,9/13/2024,16,8.3 方程求解,dsolve(D2y = -a2*y, y(0) = 1, Dy(pi/a) = 0),ans=,cos(a*t),dsolve(Dx = y, Dy = -x),x=,cos(t)*C1+sin(t)*C2,y =,-sin(t)*C1+cos(t)*C2,9/13/2024,17,8.4 线性代数运算,matlab中大多数用于数值线性代数计算的命令，都可以用于符号变量线性代数的运算。,9/13/2024,18,8.5 其它命令,因式分解（factor）,factor(X),如：,factor(x3-y3),ans=,(x-y)*(x2+x*y+y2),9/13/2024,19,8.5 其它命令,factor(a2-b2, a3+b3),ans=,(a-b)*(a+b), (a+b)*(a2-a*b+b2),factor(sym(123456789),ans= (2)*(3)2*(5)*(101)*(3803)*(3607)*(27961)*(3541),9/13/2024,20,8.5 其它命令,函数求逆（finverse）,格式：,g = finverse(f),g = finverse(f,u),如：,finverse(1/tan(x),ans=,atan(1/x),9/13/2024,21,8.5 其它命令,数值多项式转化为符号多项式(poly2sym),r = poly2sym(c),r = poly2sym(c, v),符号多项式转化为数值多项式(sym2poly),c = sym2poly(s),9/13/2024,22,