分类：
2008-06-07 23:27:18
【1】求的Laplace变换。
syms t s;syms a b positive %对常数进行“限定性”设置 <1>
Dt=sym('Dirac(t-a)'); %<2>
Ut=sym('Heaviside(t-b)'); %<3>
Mt=[Dt,Ut;exp(-a*t)*sin(b*t),t^2*exp(-t)];MS=laplace(Mt,t,s)
MS =
[ exp(-a*s), exp(-b*s)/s]
[ b/((s+a)^2+b^2), 2/(1+s)^3]
【2】验证Laplace时移性质： 。
syms t s;t0=sym('t0','positive'); %<1>
ft=sym('f(t-t0)')*sym('Heaviside(t-t0)')
FS=laplace(ft,t,s),FS_t=ilaplace(FS,s,t)
ft =
f(t-t0)*Heaviside(t-t0)
FS =
exp(-s*t0)*laplace(f(t),t,s)
FS_t =
f(t-t0)*Heaviside(t-t0)
