Laplace Transforms and Their Applications to Differential Equations

by N.W. McLachlan

Overview

This introduction to modern operational calculus offers a classic exposition of Laplace transform theory and its application to the solution of ordinary and partial differential equations. The treatment is addressed to graduate students in engineering, physics, and applied mathematics and may be used as a primary text or supplementary reading.
Chief topics include the theorems or rules of the operational calculus, evaluation of integrals and establishment of mathematical relationships, derivation of Laplace transforms of various functions, the Laplace transform for a finite interval, and other subjects. Many problems and illustrative examples appear throughout the book, which is further augmented by helpful Appendixes.

Product Details

ISBN-13:	9780486798233
Publisher:	Dover Publications
Publication date:	08/20/2014
Series:	Dover Books on Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	240
File size:	43 MB
Note:	This product may take a few minutes to download.

About the Author

Norman William McLachlan taught electrical engineering at the University of Illinois and the University of Washington. He wrote several books on engineering-related mathematics and other topics.

Table of Contents

Prefaces iii

Symbols xi

Foreword xiii

I The Laplace Transform 1

II Theorems or Rules of the Operational Calculus 18

III Solution of Ordinary Linear Differential Equations with Constant Coefficients 49

IV Solution of Partial Linear Differential Equations with Constant Coefficients 63

V Evaluation of Integrals and Establishment of Mathematical Relationships 100

VI Derivation of Laplace Transforms of Various Functions 116

VII Laplace Transform for a Finite Interval: Impulses 129

Foreword to Appendices 145

Appendix I Heaviside's Unit Function 147

Appendix II Convergence of Infinite Series 149

Appendix III Convergence of Infinite Integrals 155

Appendix IV Particular Case of Mellin Inversion Theorem 177

Appendix V Proof that L.T. Method Gives Correct Solution of Ordinary Linear Differential Equations with Constant Coefficients 179

Appendix VI Solution of Differential Equation for Impulsive Force I(T), When That for Unit Function is Known 182

Examples to be Worked Out (With Answers) 184

Short List of Laplace Transforms (81) 208

References 212

Index 213