15.1 Error Function

15.2 Laplace Transform

15.3 Fourier Integral

15.4 Fourier Transforms

15.5 Finite Fourier Transforms

15.6 Fast Fourier Transform

Chapter 15 in Review

The method of separation of variables is a powerful, but not universally applicable, method for solving boundary-value problems (BVPs). If the partial differential equation (PDE) is nonhomogeneous, or the boundary conditions are time dependent, or the domain of the spatial variable is the infinite interval (−, ) or a semi-infinite interval (a, ), we may be able to use an integral transform to solve the problem. In Section 15.2 we will solve BVPs that involve the heat and wave equations by means of the Laplace transform. In Sections 15.4 and 15.5 we introduce five new integral transforms: three Fourier transforms and two finite Fourier transforms.