Appendix C.3. The Laplace transform and inverse

The Laplace transform is given by

If L[f] is the laplace transform of f then the inverse transform is given by

where c is a real number greater than all of the real parts of the singularities of L[f](s) (see [50, 54]). The inverse is found by applying the Fourier-Mellin inversion theorem, [14].