MATLAB2014b第二章部分答案

4. (1)

syms x positive

assumeAlso(x,'integer')

f1=x^4-5.1*x^3+58.04*x^2-264.384*x+321.408; r1=solve(f1)

(2)

syms x clear

syms a positive

solve(x^2-a*x+a^2)

5. A=sym('[a11,a12,a13;a21,a22,a23;a31,a32,a33]')

或 A=sym('a%d%d',[3,3])

Dt=det(A)

Iv=inv(A)

[Ivs,d]=subexpr(Iv,'d')

6. syms x k

f=x^k;

s=symsum(f,k,0,inf)

subs(s,x,{sym('-1/3'),sym('1/pi'),sym('3')})

7. syms k

syms x positive

f=2/(2*k+1)*((x-1)/(x+1))^(2*k+1);

s=simple(symsum(f,k,0,inf))

8. syms t

y=abs(sin(t))

d=diff(y)

d0=limit(d,t,0,'left')

d1=limit(d,t,pi/2) (or subs(d,t,sym('pi/2'))) 9. syms x clear

syms x

f=exp(-abs(x))*abs(sin(x))

vpa(int(f,x,-5*pi,1.7*pi),64)

10. syms x y

int(int(f,y,1,x^2),x,1,2)

11. syms t x

f=sin(t)/t

y=int(f,t,0,x)

y5=subs(y,x,sym('4.5'))

ezplot(y,[0,2*pi])

12. syms x

syms n positive

f=sin(x)^n

y=int(f,x,0,pi/2)

ys=vpa(subs(y,n,sym('1/3')))

yd=vpa(subs(y,n,1/3))

13. syms a b k n

x=a^k; h=b^k;

f=subs(h,k,n)*subs(x,k,k-n)

y=symsum(f,n,0,k)

15. syms A t w

syms a positive

ft=A*exp(-a*abs(t));

Fw=fourier(ft,t,w)

16. syms t A w

syms tao positive

ft=A*((1+t/tao)*(heaviside(t+tao)-heaviside(t))+(1-t/tao)*(heaviside(t)-heaviside(t-tao)));

Fw=simple(fourier(ft,t,w))

Fw1=simple(subs(Fw,[A,tao],[2,2]))

ezplot(Fw1)

17. syms s t

Fs=(s+3)/(s^3+3*s^2+6*s+4)

ft=ilaplace(Fs, s,t)

18. syms t s

y=sym('f(t)')

Ldy=laplace(df,t,s)

20. [x,y]=solve('x^2+y^2=1','x*y=2','x','y')

24. x=dsolve('Dx=a*t^2+b*t','x(0)=2')

25. [f,g]=dsolve('Df=3*f+4*g','Dg=-4*f+3*g','f(0)=0','g(0)=1','x')