When does Fourier Transform be the same as Laplace's?

Question

I have the TI nspire CX CAS... it can perform Laplace Transform but can't perform Fourier Transform. They are equal in some problems, but not all the time! So, when does both of them be equal so that I can use Laplace for F.Ts?

Thanks in advance

Answer 1

The continuous Fourier transform is equivalent to evaluating the bilateral Laplace transform with imaginary argument s = iω or s = 2πfi, per this wikipedia page:

http://en.wikipedia.org/wiki/Laplace_transform#Fourier_transform

So you can perform the Laplace Transform, then make the imaginary substitution in the result.