Laplace Transforms

Abstract

In Chap. 10 we learned how to solve certain differential equations of the first and second order.We now consider a special technique for the solution of such ordinary differential equations known as the Laplace transform. It was first introduced by the French mathematician P. S. de Laplace in about 1780. The main advantage of the method is that it transforms the DE into an algebraic equation which, in many cases, can be readily solved. The solution of the original DE is then arrived at by obtaining the inverse transforms which usually consist of the ratio of two polynomials. The transforms and their inverses can be derived or obtained by consulting a table of transforms. We shall build up such a table of the functions frequently met in practice.