What are the differences between laplace & fourier transform

1. May 23, 2006

serimc

What are the differences?
I mean when we will make a decision "hmm now i must use laplace transform or now i must use fourier transform".

What are the absences in laplace transform so fourier design a new transfom?

I want to know these transforms' main idea, differences.

Thanks .
Sincerely;

2. May 27, 2006

JohanL

in applications you usually use Laplace transforms when you have initial conditions for a p.d.e. and u start at t=0. Thats because when you Laplace transform derivatives you get the initial conditions into the p.d.e.

Often you Fourier-Laplace transforms differential equations too. If you have a p.d.e. for u(r,t) you can Fourier transform the position and Laplace transform the time. Then you get an easier equation for
u(k,z), where k is the wave-vector. This is very useful when you want to derive the Greenfunction for a particular problem.