Laplace Transforms

Abstract

In this chapter we shall show how the Laplace transform operational methods apply to the analysis of transport phenomena. We shall trace the definition of the Laplace transform to its application with various functional forms. The Laplace transform technique will then be shown in the handling of ordinary and partial differential equations. Finite difference equations, integral, integrodifferential, and differential-difference equations are also treated. A discussion of methods of inverting Laplace transforms leads to a review of complex variables, since one of the methods for finding inverse Laplace transforms involves integration in the complex plane. Many examples are shown illustrating the procedures for finding the inverse Laplace transform. This chapter concludes with a discussion of the difficulties encountered when the Laplace transform technique for solving differential equations is applied to nonlinear equations.