Engineering Mathematics

19

Laplace Transforms

19.0 INTRODUCTION

Laplace transform is a powerful tool for solving linear differential equations. Laplace transform converts a linear differential equation with initial conditions to an algebraic problem. This process of changing from operations of calculus to algebraic operations on transforms is known as operational calculus, which is an important area of applied mathematics. The advantage of Laplace transforms in solving initial value problems lies in the fact that the initial conditions are taken care of at the outset and the solution is directly obtained without resorting to finding the general solution and then the arbitrary constants.

The name is due to the French mathematician Pierre Simon de Laplace who used this ...