《高等应用数学问题的MATLAB求解》——第5章习题代码

（1）

>> syms t alpha a beta theta;
>> fa=sin(alpha*t)/t;
>> fb=t^5*sin(alpha*t);
>> fc=t^6*exp(alpha*t);
>> fd=t^6*exp(alpha*t);
>> fe=5*exp(-a*t)+t^4*exp(-a*t)+8*exp(-2*t);
>> ff=exp(beta*t)*sin(alpha*t+theta);
>> fg=exp(-12*t)+6*exp(9*t);
>> Lfa=laplace(fa); Lfb=laplace(fb); Lfc=laplace(fc); Lfd=laplace(fd); Lfe=laplace(fe); Lff=laplace(ff); Lfg=laplace(fg);
>> Lfa,Lfb,Lfc,Lfd,Lfe,Lff,Lfg

（2）接上一题

fa2=ilaplace(Lfa); fb2=ilaplace(Lfb); fc2=ilaplace(Lfc); fd2=ilaplace(Lfd); fe2=ilaplace(Lfe); ff2=ilaplace(Lff); fg2=ilaplace(Lfg);

（3）

>> syms t s f(t); n=2; %修改n的取值
>> simplify(laplace(t^n*f(t),t,s)-(-1)^n*diff(laplace(f(t),t,s),s,n))

（4）

>> syms t s a b alpha;
>> Fa(s)=1/(sqrt(s)*(s^2-a^2)*(s+b));
>> Fb(s)=sqrt(s-a)-sqrt(s-b);
>> Fc(s)=log((s-a)/(s-b));
>> Fd(s)=1/(sqrt(s)*(s+a));
>> Fe(s)=3*a^2/(s^3+a^3);
>> Ff(s)=(s-10)^8/s^7;
>> Fg(s)=log((s^2+a^2)/(s^2+b^2));
>> Fh(s)=s^2+3*s+8;for k=1:1:8,Fh(s)=Fh(s)/(s+k); end;
>> Fi(s)=(s+a)/(2*(s-a));
>> fa(t)=ilaplace(Fa(s),s,t); fb(t)=ilaplace(Fb(s),s,t); fc(t)=ilaplace(Fc(s),s,t); fd(t)=ilaplace(Fd(s),s,t); fe(t)=ilaplace(Fe(s),s,t); ff(t)=ilaplace(Ff(s),s,t); fg(t)=ilaplace(Fg(s),s,t); fh(t)=ilaplace(Fh(s),s,t); fi(t)=ilaplace(Fi(s),s,t);

（5）