Background Mathematics

Abstract

The companion volume of this book, ‘Analytic methods for partial differential equations’, is concerned with solution of partial differential equations using classical methods which result in analytic solutions. These equations result when almost any physical situation is modelled, ranging from fluid mechanics problems, through electromagnetic problems to models of the economy. Some specific and fundamental problems were highlighted in the earlier volume, namely the three major classes of linear second order partial differential equations. The heat equation, the wave equation and Laplace’s equation will form a basis for study from a numerical point of view for the same reason as they did in the analytic case. That is, the three equations are the canonical forms to which any quasi-linear second order equation may be reduced using the characteristic transformation.