Differential Equations, 3rd Edition

8Laplace Transforms

DOI: 10.1201/9781003214526-8

• The idea of the Laplace transform

• The Laplace transform and differential equations

• Derivatives and the Laplace transform

• Integrals and the Laplace transform

• Convolutions

• Step and impulse functions

• Discontinuous input

8.0 Introduction

The idea of the Laplace transform has had a profound influence on the development of mathematical analysis. It also plays a significant role in mathematical applications. More generally, the overall theory of transforms has become an important part of modern mathematics.

The concept of a transform is that it turns a given function into another function. We are already acquainted with several transforms:

1. The derivative D takes a differentiable function f (defined ...