  After discussing the limitations of current commercial software, we provide
the details of an implementation of Fourier techniques for solving second-order
linear partial differential equations (with constant coefficients) using a
computer algebra system. The general Sturm-Liouville problem for the heat, wave
and Laplace operators on the most common bounded domains is covered, as well as
the general second-order linear parabolic equation with constant coefficients,
which includes cases such as the convection-diffusion equation by reduction to
the heat equation.
