• PROPERTIES OF GENERALIZED FOURIER-LAPLACE TRANSFORM

Abstract

Fourier and Laplace transforms are examples of mathematical operations which can play an important role in the analysis of mathematical models for problems originating from a broad spectrum of fields. These transforms are certainly not new, but the strong development of digital computers has given a new impulse to both the applications and the theory. An integral transform is useful if it allows one to turn a complicated problem into a simpler one. The transforms we will be studying in this part of the course are mostly useful to solve differential and, to a lesser extent, integral equations. The specific Fourier and Laplace transform being used may differ from application to application. For electrical network the Fourier and Laplace transforms are applied to functions describing a current or voltage as function of time. They are also useful in physical problems, such as heat conduction and analyzing the transfer of signals in various systems.