MATLAB结果：
>> syms t;
A=[-4.5,0,0.5,-1.5;-0.5,-4,0.5,-0.5;1.5,1,-2.5,1.5;0,-1,-1,-3]; B=simple(expm(A*t)) C=simple(sin(A*t))
D=simple(expm(A*t)*sin(A^2*expm(A*t)*t)) B =
[ 1/2/exp(t)^3-1/2*t/exp(t)^3+1/2/exp(t)^5+1/2*t^2/exp(t)^3, 1/2/exp(t)^5-1/2/exp(t)^3+t/exp(t)^3,
1/2*t/exp(t)^3+1/2*t^2/exp(t)^3, 1/2/exp(t)^5-1/2/exp(t)^3-1/2*t/exp(t)^3+1/2*t^2/exp(t)^3]
[ 1/2*t/exp(t)^3+1/2/exp(t)^5-1/2/exp(t)^3, 1/2/exp(t)^3+1/2/exp(t)^5, 1/2*t/exp(t)^3, 1/2*t/exp(t)^3+1/2/exp(t)^5-1/2/exp(t)^3]
[ 1/2*t/exp(t)^3-1/2/exp(t)^5+1/2/exp(t)^3, -1/2/exp(t)^5+1/2/exp(t)^3, 1/exp(t)^3+1/2*t/exp(t)^3, 1/2*t/exp(t)^3-1/2/exp(t)^5+1/2/exp(t)^3]
[ -1/2*t^2/exp(t)^3, -t/exp(t)^3, -1/2*t^2/exp(t)^3-t/exp(t)^3, 1/exp(t)^3-1/2*t^2/exp(t)^3] C =
[ -sin(9/2*t), 0, sin(1/2*t), -sin(3/2*t)] [ -sin(1/2*t), -sin(4*t), sin(1/2*t), -sin(1/2*t)] [ sin(3/2*t), sin(t), -sin(5/2*t), sin(3/2*t)]
[ 0, -sin(t), -sin(t), -sin(3*t)] D =
[ (1/2*exp(-3*t)-1/2*t*exp(-3*t)+1/2*exp(-5*t)+1/2*t^2*exp(-3*t))*sin(t*(17/2*exp(-3*t)-21/2*t*exp(-3*t)+25/2*exp(-5*t)+9/2*t^2*exp(-3*t)))+(1/2*exp(-5*t)-1/2*exp(-3*t)+t*exp(-3*t))*sin(t*(-15/2*exp(-3*t)+9/2*t*exp(-3*t)+25/2*exp(-5*t)))+(1/2*t*exp(-3*t)+1/2*t^2*exp(-3*t))*sin(t*(3/2*exp(-3*t)+9/2*t*exp(-3*t)-25/2*exp(-5*t)))+(1/2*exp(-5*t)-1/2*exp(-3*t)-1/2*t*exp(-3*t)+
1/2*t^2*exp(-3*t))*sin(t*(-exp(-3*t)+6*t*exp(-3*t)-9/2*t^2*exp(-3*t))), (1/2*exp(-3*t)-1/2*t*exp(-3*t)+1/2*exp(-5*t)+1/2*t^2*exp(-3*t))*sin(t*(25/2*exp(-5*t)-21/2*exp(-3*t)+9*t*exp(-3*t)))+(1/2*exp(-5*t)-1/2*exp(-3*t)+t*exp(-3*t))*sin(t*(25/2*exp(-5*t)+9/2*exp(-3*t)))+(1/2*t*exp(-3*t)+1/2*t^2*exp(-3*t))*sin(t*(-25/2*exp(-5*t)+9/2*exp(-3*t)))+(1/2*exp(
-5*t)-1/2*exp(-3*t)-1/2*t*exp(-3*t)+1/2*t^2*exp(-3*t))*sin(t*(6*exp(-3*t)-9*t*exp(-3*t))), (1/2*exp(-3*t)-1/2*t*exp(-3*t)+1/2*exp(-5*t)+1/2*t^2*exp(-3*t))*sin(t*(-3/2*t*exp(-3*t)+9/2*t^2*exp(-3*t)-2*exp(-3*t)))+(1/2*exp(-5*t)-1/2*exp(-3*t)+t*exp(-3*t))*sin(t*(9/2*t*exp(-3*t)-3*exp(-3*t)))+(1/2*t*exp(-3*t)+1/2*t^2*exp(-3*t))*sin(t*(9/2*t*exp(-3*t)+6*exp(-3*t)))+(1/2*exp(-5*t)-1/2*exp(-3*t)-1/2*t*exp(-3*t)+1/2*t^2*exp(-3*t))*sin(t*(-3*t*exp(-3*t)-9/2*t^2*exp(-3*t)+5*exp(-3*t))),
(1/2*exp(-3*t)-1/2*t*exp(-3*t)+1/2*exp(-5*t)+1/2*t^2*exp(-3*t))*sin(t*(25/2*exp(-5*t)-1/2*exp(-3*t)-21/2*t*exp(-3*t)+9/2*t^2*exp(-3*t)))+(1/2*exp(-5*t)-1/2*exp(-3*t)+t*exp(-3*t))*sin(t*(-15/2*exp(-3*t)+9/2*t*exp(-3*t)+25/2*exp(-5*t)))+(1/2*t*exp(-3*t)+1/2*t^2*exp(-3*t))*sin(t*(3/2*exp(-3*t)+9/2*t*exp(-3*t)-25/2*exp(-5*t)))+(1/2*exp(-5*t)-1/2*exp(-3*t)-1/2*t*exp(-3*t)+1/2*t^2*exp(-3*t))*sin(t*(8*exp(-3*t)+6*t*exp(-3*t)-9/2*t^2*exp(-3*t)))]
[ (1/2*t*exp(-3*t)+1/2*exp(-5*t)-1/2*exp(-3*t))*sin(t*(17/2*exp(-3*t)-21/2*t*exp(-3*t)+25/2*exp(-5*t)+9/2*t^2*exp(-3*t)))+(1/2*exp(-3*t)+1/2*exp(-5*t))*sin(t*(-15/2*exp(-3*t)+9/2*t*exp(-3*t)+25/2*exp(-5*t)))+1/2*t*exp(-3*t)*sin(t*(3/2*exp(-3*t)+9/2*t*exp(-3*t)-25/2*exp(-5*t)))+(1/2*t*exp(-3*t)
+1/2*exp(-5*t)-1/2*exp(-3*t))*sin(t*(-exp(-3*t)+6*t*exp(-3*t)-9/2*t^2*exp(-3*t))), (1/2*t*exp(-3*t)+1/2*exp(-5*t)-1/2*exp(-3*t))*sin(t*(25/2*exp(-5*t)-21/2*exp(-3*t)+9*t*exp(-3*t)))+(1/2*exp(-3*t)+1/2*exp(-5*t))*sin(t*(25/2*exp(-5*t)+9/2*exp(-3*t)))+1/2*t*exp(-3*t)*sin(t*(-25/2*exp(-5*t)+9/2*exp(-3*t)))+(1/2*t*exp(-3*t)+1/2*exp(-5*t)-1/2*exp(-3*t))*sin(t*(6*exp(-3*t)-9*t*exp(-3*t))), (1/2*t*exp(-3*t)+1/2*exp(-5*t)-1/2*exp(-3*t))*sin(t*(-3/2*t*exp(-3*t)+9/2*t^2*exp(-3*t)-2*exp(-3*t)))+(1/2*exp(-3*t)+1/2*exp(-5*t))*sin(t*(9/2*t*exp(-3*t)-3*exp(-3*t)))+1/2*t*exp(-3*t)*sin(t*(9/2*t*exp(-3*t)+6*exp(-3*t)))+(1/2*t*exp(-3*t)+1/2*exp(-5*t)-1/2*exp(-3*t))*sin(t*(-3*t*exp
(-3*t)-9/2*t^2*exp(-3*t)+5*exp(-3*t))), (1/2*t*exp(-3*t)+1/2*exp(-5*t)-1/2*exp(-3*t))*sin(t*(25/2*exp(-5*t)-1/2*exp(-3*t)-21/2*t*exp(-
3*t)+9/2*t^2*exp(-3*t)))+(1/2*exp(-3*t)+1/2*exp(-5*t))*sin(t*(-15/2*exp(-3*t)+9/2*t*exp(-3*t)+25/2*exp(-5*t)))+1/2*t*exp(-3*t)*sin(t*(3/2*exp(-3*t)+9/2*t*exp(-3*t)-25/2*exp(-5*t)))+(1/2*t*exp(-3*t)+1/2*exp(-5*t)-1/2*exp(-3*t))*sin(t*(8*exp(-3*t)+6*t*exp(-3*t)-9/2*t^2*exp(-3*t)))]
[ (1/2*t*exp(-3*t)-1/2*exp(-5*t)+1/2*exp(-3*t))*sin(t*(17/2*exp(-3*t)-21/2*t*exp(-3*t)+25/2*exp(-5*t)+9/2*t^2*exp(-3*t)))+(-1/2*exp(-5*t)+1/2*exp(-3*t))*sin(t*(-15/2*exp(-3*t)+9/2*t*exp(-3*t)+25/2*exp(-5*t)))+(exp(-3*t)+1/2*t*exp(-3*t))*sin(t*(3/2*exp(-3*t)+9/2*t*exp(-3*t)-25/2*exp(-5*t)))+(1/2*t*exp(-3*t)-1/2*exp(-5*t)+1/2*exp(-3*t))*sin(t*(-exp(-3*t)+6*t*exp(-3*t)-9/2*t^2*exp(-3*t))), (1/2*t*exp(-3*t)-1/2*exp(-5*t)+1/2*exp(-3*t))*sin(t*(25/2*exp(-5*t)-21/2*exp(-3*t)+9*t*exp(-3*t)))+(-1/2*exp(-5*t)+1/2*exp(-3*t))*sin(t*(25/2*exp(-5*t)+9/2*exp(-3*t)))+(exp(-3*t)+1/2*t*exp(-3*t))*sin(t*(-25/2*exp(-5*t)+9/2*exp(-3*t)))+(1/2*t*exp(-3*t)-1/2*exp(-5*t)+1/2*exp(-3*t))*
sin(t*(6*exp(-3*t)-9*t*exp(-3*t))), (1/2*t*exp(-3*t)-1/2*exp(-5*t)+1/2*exp(-3*t))*sin(t*(-3/2*t*exp(-3*t)+9/2*t^2*exp(-3*t)-2*exp(-3*t)))+(-1/2*exp(-5*t)+1/2*exp(-3*t))*sin(t*(9/2*t*exp(-3*t)-3*exp(-3*t)))+(exp(-3*t)+1/2*t*exp(-3*t))*sin(t*(9/2*t*exp(-3*t)+6*exp(-3*t)))+(1/2*t*exp(-3*t)-1/2*exp(-5*t)+1/2*exp(-3*t))*sin
(t*(-3*t*exp(-3*t)-9/2*t^2*exp(-3*t)+5*exp(-3*t))), (1/2*t*exp(-3*t)-1/2*exp(-5*t)+1/2*exp(-3*t))*sin(t*(25/2*exp(-5*t)-1/2*exp(-3*t)-21/2*t*exp(-3*t)+9/2*t^2*exp(-3*t)))+(-1/2*exp(-5*t)+1/2*exp(-3*t))*sin(t*(-15/2*exp(-3*t)+9/2*t*exp(-3*t)+25/2*exp(-5*t)))+(exp(-3*t)+1/2*t*exp(-3*t))*sin(t*(3/2*exp(-3*t)+9/2*t*exp(-3*t)-25/2*exp(-5*t)))+(1/2*t*exp(-3*t)-1/2*exp(-5*t)+1/2*exp(-3*t))*sin(t*(8*exp(-3*t)+6*t*exp(-3*t)-9/2*t^2*exp(-3*t)))]
[
-1/2*t^2*exp(-3*t)*sin(t*(17/2*exp(-3*t)-21/2*t*exp(-3*t)+25/2*exp(-5*t)+9/2*t^2*exp(-3*t)))-t*exp(-3*t)*sin(t*(-15/2*exp(-3*t)+9/2*t*exp(-3*t)+25/2*exp(-5*t)))+(-1/2*t^2*exp(-3*t)-t*exp(-3*t))*sin(t*(3/2*exp(-3*t)+9/2*t*exp(-3*t)-25/2*exp(-5*t)))+(exp(-3*t)-1/2*t^2*exp(-3*t))*sin(t
*(-exp(-3*t)+6*t*exp(-3*t)-9/2*t^2*exp(-3*t))), -1/2*t^2*exp(-3*t)*sin(t*(25/2*exp(-5*t)-21/2*exp(-3*t)+9*t*exp(-3*t)))-t*exp(-3*t)*sin(t*(25/2*exp(-5*t)+9/2*exp(-3*t)))+(-1/2*t^2*exp(-3*t)-t*exp(-3*t))*sin(t*(-25/2*exp(-5*t)+9/2*exp(-3*
t)))+(exp(-3*t)-1/2*t^2*exp(-3*t))*sin(t*(6*exp(-3*t)-9*t*exp(-3*t))), -1/2*t^2*exp(-3*t)*sin(t*(-3/2*t*exp(-3*t)+9/2*t^2*exp(-3*t)-2*exp(-3*t)))-t*exp(-3*t)*sin(t*(9/2*t*exp(-3*t)-3*exp(-3*t)))+(-1/2*t^2*exp(-3*t)-t*exp(-3*t))*sin(t*(9/2*t*exp(-3*t)+6*exp(-3*t)
))+(exp(-3*t)-1/2*t^2*exp(-3*t))*sin(t*(-3*t*exp(-3*t)-9/2*t^2*exp(-3*t)+5*exp(-3*t))), -1/2*t^2*exp(-3*t)*sin(t*(25/2*exp(-5*t)-1/2*exp(-3*t)-21/2*t*exp(-3*t)+9/2*t^2*exp(-3*t)))-t*exp(-3*t)*sin(t*(-15/2*exp(-3*t)+9/2*t*exp(-3*t)+25/2*exp(-5*t)))+(-1/2*t^2*exp(-3*t)-t*exp(-3*t))*sin(t*(3/2*exp(-3*t)+9/2*t*exp(-3*t)-25/2*exp(-5*t)))+(exp(-3*t)-1/2*t^2*exp(-3*t))*sin(t*(8*exp(-3*t)+6*t*exp(-3*t)-9/2*t^2*exp(-3*t)))]
第二部分
1、对下列的函数f(t)进行Laplace变换。 （1）fa(t)?sin?t；（2）fb(t)?t5sin?t；（3）fc(t)?t8cos?t。 tMATLAB结果：
（1）fa(t)?sin?t t>>syms t alpha;f=sin(alpha*t)/t;F=laplace(f) F =
atan(alpha/s)
（2）fb(t)?t5sin?t
>>syms t alpha;f=t^5*sin(alpha*t);F=laplace(f) F =
120/(s^2+alpha^2)^3*sin(6*atan(alpha/s)) （3）fc(t)?t8cos?t
>>syms t alpha;f=t^8*cos(alpha*t);F=laplace(f) F =
40320/(s^2+alpha^2)^(9/2)*cos(9*atan(alpha/s)) 2、对下面的F(s)式进行Laplace反变换。 （1）Fa(s)?1s(s?a)(s?b)222；
（2）Fb(s)?s?a?s?b；
（3）Fc(s)?lns?a。 s?bMATLAB结果：
(1)Fa(s)? >> syms s a b;
f=1/(sqrt(s^2)*(s^2-a^2)*(s+b)); F=ilaplace(f) F =
-1/2/(a-b)/a^2*exp(-a*t)+1/2/(a+b)/a^2*exp(a*t)-1/a^2/b+1/b/(a^2-b^2)*exp(-b*t) (2)Fb(s)? >> syms s a b; f=sqrt(s-a)-sqrt(s-b); F=ilaplace(f) F =
1/2/t/(t*pi)^(1/2)*(exp(b*t)-exp(a*t)) (3)Fc(s)?ln
s?b >> syms s a b; f=log((s-a)/(s-b)); F=ilaplace(f) F =
(exp(b*t)-exp(a*t))/t
3、试求出下面函数的Fourier变换，对得出的结果再进行Fourier反变换，观察是否能得
1s(s?a)(s?b)222
s?a?s?b
s?a