ABSTRACT
In this chapter, we present the basic principles of the Laplace transform and its inversion theorem, with emphasis on their utilization for solving transient heat conduction applications.We first give a brief introduction to commonly utilized methods for obtaining the forward Laplace transform and its inversion. Tables of transforms, analytical transform methods and numerical procedures are outlined. Next, we discuss two application examples describing heat conduction in a finite region and in an infinite region. The aim of these examples is to show how the Laplace transform provides simple tools for solving partial differential equations, but in the meanwhile, we show how the inversion might lead to rather complicated inverse transform integrals, which require rigorous computational tools to tackle.
