Past Workshops With Industry

21 October 2005
Taking a view common in the finite element analysis, we interpret the first N terms of the usual Fourier series solution as the exact solution of an approximating problem in a subspace spanned by the eigenfunctions of the underlying Sturm Liouville problem. This view leads to a consistent solution technique for the heat, wave and Poisson's equation, and allows an analysis of the error caused by truncating the Fourier series. Applications to a variety of problems will be discussed to demonstrate that the analytic approach remains a valuable complement to purely numerical methods. The talk is intended for students with an interest in actually solving partial differential equations. It assumes a standard background in undergraduate mathematics but not necessarily prior exposure to the subject. The goal is to show that there is more to separation of variables than is apparent from standard texts on engineering mathematics.
  • Workshops With Industry