We were discussing this in a comm systems class yesterday and no one could come up with a good explaination as to why we use Laplace transforms over Fourier and vice versa. Both take equations that are in the time domain and transform them into the frequency domain. It seems in Comm we use only Fourier analysis methods and in Circuit analysis and DE we onle use Laplace.

What are the situations that define which one you will use?

On a side note, what are Z transforms typically used for?