Partial Differential Equations

Abstract

AbstractIn previous chapters, we have explained how ordinary differential equations can be solved using Laplace transforms. In Chap. 4, Fourier series were introduced, and the important property that any reasonable function can be expressed as a Fourier series derived. In this chapter, these ideas are brought together, and the solution of certain types of partial differential equation using both Laplace transforms and Fourier series are explored. The study of the solution of partial differential equations (abbreviated PDEs) is a vast topic that it is neither possible nor appropriate to cover in a single chapter. There are many excellent texts (Weinberger (1965), Sneddon (1957) and Williams (1980) to name but three) that have become standard. Here we shall only be interested in certain types of PDE that are amenable to solution by Laplace transform.KeywordsPartial Differential EquationWave EquationFourier SeriesHeat Conduction EquationAsymptotic SeriesThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.