Laplace transform

Abstract

In this chapter we study some basic properties of the Laplace Transform, (or L-Transform for short), which plays an important role not only in mathematics but also in the sciences and engineering. This is a deep subject and a rigorous and thorough treatment of it would be beyond the scope of this book. So we will not venture too far beyond some of its basic properties. In particular, we will discuss its application in solving initial value problems for linear differential equations with constant coefficients. This powerful method essentially consists of converting an initial value problem to an algebraic equation involving the Laplace Transform X of the solution x to the differential equation, and then recovering the solution x by taking the inverse of X.