# Laplace Transform

1. May 4, 2007

### Neoon

Hi all,

Just a small question:
I came across a problem to solve a differential equation using Laplace transform.

I solved the major part but only still a part where I had to inverse transform the following experssion:

(exp(-s))/(s^2)

I looked in Laplace Transform Tables but did not find it.

2. May 7, 2007

### tpm

think i got it..

you're looking for the integral..

$$(2\pi i)^{-1} \oint ds exp(-st-s)/s^{2}$$

now using 'Residue theorem' you get...

$$f(t)=0$$ iff t<1 and f(t)=t/2 [/tex] iff t>1.

depending on if you take the semi-circle (-T,0) or (0,T) with T--->oo , there is a double pole at s=0