5Transform theory

IB Complex Methods

5 Transform theory
We are now going to consider two different types of “transforms”. The first
is the Fourier transform, which we already met in IB methods. The second is
the Laplace transform. While the formula of a Laplace transform is completely
real, the inverse Laplace transform involves a more complicated contour integral,
which is why we did not do it in IB Methods. In either case, the new tool of
contour integrals allows us to compute more transforms.
Apart from that, the two transforms are pretty similar, and most properties
of the Fourier transform also carry over to the Laplace transform.