第八讲MATLAB符号运算

1、第八讲 MATLAB符号运算7/23/20227/23/20221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7/23/202228.1 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 . realsyms arg1 arg2 . unreal7/23/202238.2 微分积分运算2.1微分diff(S,v) （s对变量v求偏导）diff(S,n) （

2、对s求n次导）diff(S,v,n)（s对变量 v 求n 次偏导）7/23/202248.2 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)7/23/202258.2 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)7/23/202268.2 微分积分运算int(x/(1+z2),z) ans= atan(z)*xint(x*log(1+x)

3、,0,1)ans= 1/4int(2*x, sin(t), 1) ans= 1-sin(t)27/23/202278.2 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)7/23/202288.2 微分积分运算例如： syms x a t h;limit(sin(x)/x) = 1limit(1/x,x,0,right) = infli

4、mit(1/x,x,0,left) = -inflimit(sin(x+h)-sin(x)/h,h,0) = cos(x)7/23/202298.2 微分积分运算v = (1 + a/x)x, exp(-x);limit(v,x,inf,left) = exp(a), 02.4.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+1/67/23/2022108.3 方程求解3.解方程3.1代数方程（solve）g = solve(eq)g = solve(eq,var)g = solve

5、(eq1,eq2,.,eqn)g = solve(eq1,eq2,.,eqn,var1,var2,.,varn)7/23/2022118.3 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)/xsolve(x + y = 1,x - 11*y = 5) y = -1/3, x = 4/37/23/2022128.3 方程求解A = solve(a*u2 + v2, u - v = 1, a2 -

6、5*a + 6)A = a: 1x4 sym u: 1x4 sym v: 1x4 sym这里A.a = 2, 2, 3, 37/23/2022138.3 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)7/23/2022148.3 方程求解3.2微分方程（dsolve） r = dsolve(eq1,eq2,., cond1,

7、cond2,., v)r = dsolve(eq1,eq2,.,cond1,cond2,.,v)如：dsolve(Dy = a*y) ans= exp(a*t)*C1 7/23/2022158.3 方程求解dsolve(Df = f + sin(t) ans= -1/2*cos(t)-1/2*sin(t)+exp(t)*C1dsolve(Dy)2 + y2 = 1,s) ans= -sin(-s+C1)dsolve(Dy = a*y, y(0) = b) ans= exp(a*t)*b 7/23/2022168.3 方程求解dsolve(D2y = -a2*y, y(0) = 1, Dy(pi

8、/a) = 0) ans= cos(a*t) dsolve(Dx = y, Dy = -x) x= cos(t)*C1+sin(t)*C2y = -sin(t)*C1+cos(t)*C27/23/2022178.4 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。7/23/2022188.5 其它命令因式分解（factor）factor(X)如：factor(x3-y3) ans= (x-y)*(x2+x*y+y2)7/23/2022198.5 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)7/23/2022208.5 其它命令函数求逆（finverse） 格式：g = finverse(f)g = finverse(f,u)如：finverse(1/tan(x) ans