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Comprehensive presentation of Laplace transform procedures and capabilities.
"Mathematics is an essential tool in the continuing struggle to understand the physical world."
The subject of this book is the Laplace transform which is a particular mathematical transform. The Laplace transform provides an extremely powerful method for solving linear differential equations involving initial conditions. It does this by converting differential equations into algebraic equations. Differentiation is thereby replaced with algebraic manipulations. Even many differential equations having impulsive or discontinuous forcing functions can be easily solved using Laplace transforms. These transforms therefore find application in the numerous diverse fields where differential equations are used to describe changes in an entity.
The material in this book is organized and presented in a manner designed to make this a comprehensive reference work on Laplace transforms. Most of the sources for this book are given in the references at the end of the book.
"The Laplace transform is a particularly elegant way to solve linear differential equations with constant coefficients."
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#58 in Transformations Mathematics
Definition of the Laplace Transform
Properties of the Laplace Transform
Laplace Transforms of Derivatives and Integrals
Derivatives and Integrals of Laplace Transforms
Laplace Transforms of Discontinuous and Periodic Functions
Inverse Laplace Transforms
Convolution
Laplace Transforms of Series Expansions
Solution of Linear Ordinary Differential Equations having Constant Coefficients
Solution of Partial Differential Equations
Complex Variables
Inverse Laplace Transforms from Residue Integration
Solution of Linear Ordinary Differential Equations having Variable Coefficients
Evaluating Integrals Equations with the Laplace Transform
Appendicies