  We present a simple and accessible method which uses contour integration
methods to derive formulae for functional determinants. To make the
presentation as clear as possible, the general idea is first illustrated on the
simplest case: a second order differential operator with Dirichlet boundary
conditions. The method is applicable to more general situations, and we discuss
the way in which the formalism has to be developed to cover these cases. In
particular, we also show that simple and elegant formulae exist for the
physically important case of determinants where zero modes exist, but have been
excluded.
