ABSTRACT
This chapter defines the Laplace transform and discusses the use of a table of standard transforms to evaluate the transforms of elementary functions. The operation, called the Laplace transformation, provides a powerful and much used alternative method of solving linear differential equations. The solution of most electrical circuit problems reduces ultimately to the solution of differential equations. The method has many practical applications, including aspects of control engineering and coupled electrical circuits, beam problems, various electrical systems, mechanical vibration systems and in servomechanisms, and was developed by the French mathematician Pierre Simon de Laplace. Before using Laplace transforms to solve differential equations it is necessary to define the Laplace transform, to derive the transforms of elementary functions, to appreciate certain of their properties and to define and derive the inverse Laplace transform, including the use of partial fractions.
