Applied Engineering Analysis

Chapter 6Introduction to the Laplace Transform and Applications

Chapter Learning Objectives

• Learn the application of Laplace transform in engineering analysis.
• Learn the required conditions for transforming variable or variables in functions by the Laplace transform.
• Learn the use of available Laplace transform tables for transformation of functions and the inverse transformation.
• Learn to use partial fraction and convolution methods in inverse Laplace transforms.
• Learn the Laplace transform for ordinary derivatives and partial derivatives of different orders.
• Learn how to use Laplace transform methods to solve ordinary and partial differential equations.
• Learn the use of special functions in solving indeterminate beam bending problems using Laplace transform methods.

6.1 Introduction

The Laplace transform is named after Pierre-Simon Laplace (1749–1829), a renowned French mathematician and astronomer. It is a mathematical operation that is used to “transform” a variable from a variable domain to a parametric domain. In layman's terms, the Laplace transform can be used to “convert” a variable of a function into a parameter. After the transformation, that variable is no longer a variable but it can be treated as a “parameter,” which—again in layman's terms—is a “constant under specific conditions.” Transformation of variables into parameters can significantly simplify the mathematical analysis of many physical problems. A word of caution, however, is that the Laplace transform ...