* CPS- Departamento de Matemática Aplicada

Abstract:- Integral transforms are frequently used in solving physical problems which involve integral and ordinary differential equations with constant coefficients as those arising in the analysis of electronic circuits. As a consequence of this most of them not only may be quickly computed with the aid of computer algebraic systems but the most commonly used mathematical software have also got subroutines that facilitate its handling and even force the general solving methods to use them. Usually these programs enable a combined use of the integral transforms along discontinuous functions that do appear in technology such as jump functions or even distributions which are, by definition, the dual to the smooth functions of compact support, with a particular topology, and are commonly called generalized functions. One of these distributions is the delta impulse which is conveniently implemented in many programs. In this paper we are going to revisit the well known Laplace transform which finely seconds the Fourier transform in solving and analyzing physical problems in which even jumps and discontinuous functions might occur. Despite the fact that the discontinuous Heaviside functions do appear and are properly included in the solution of differential equations in which there is some delay, we will pay attention to the fact that they are commonly missed when providing the solution of casual systems in which delayed functions are not present