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.