Linear Integral Equations : Theory and Technique

Many physical problems that are usually solved by differential equation methods can be solved more effectively by integral equation methods. Such problems abound in applied mathematics, theoretical mechanics, and mathematical physics. The second edition of this widely used book continues the emphasis on applications and presents a variety of techniques with extensive examples. Additional material has been added throughout the book. The chapters dealing with differential equations and singular integral equations have been considerably expanded. Thus, the book is ideal as a text for a beginning graduate level course. Its treatment of boundary value problems and an extended, and up-to-date bibliography will also make the book useful to research workers in many applied fields. Linear Integral Equations: Theory and Technique is an 11-chapter text that covers the theoretical and methodological aspects of linear integral equations. After a brief overview of the fundamentals of the equations, this book goes on dealing with specific integral equations with separable kernels and a method of successive approximations. The next chapters explore the properties of classical Fredholm theory and the applications of linear integral equations to ordinary and partial differential equations. These topics are followed by discussions of the symmetric kernels, singular integral equations, and the integral transform methods. The final chapters consider the applications of linear integral equations to mixed boundary value problems. These chapters also look into the integral equation perturbation methods. This book will be of value to undergraduate and graduate students in applied mathematics, theoretical mechanics, and mathematical physics. Content: Front Matter, Page iii Copyright, Page iv Dedication, Page v PREFACE, Pages xi-xii CHAPTER 1 - INTRODUCTION, Pages 1-7 CHAPTER 2 - INTEGRAL EQUATIONS WITH SEPARABLE KERNELS, Pages 8-25 CHAPTER 3 - METHOD OF SUCCESSIVE APPROXIMATIONS, Pages 26-40 CHAPTER 4 - CLASSICAL FREDHOLM THEORY, Pages 41-60 CHAPTER 5 - APPLICATIONS TO ORDINARY DIFFERENTIAL EQUATIONS, Pages 61-93 CHAPTER 6 - APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS, Pages 94-131 CHAPTER 7 - SYMMETRIC KERNELS, Pages 132-166 CHAPTER 8 - SINGULAR INTEGRAL EQUATIONS, Pages 167-193 CHAPTER 9 - INTEGRAL TRANSFORM METHODS, Pages 194-213 CHAPTER 10 - APPLICATIONS TO MIXED BOUNDARY VALUE PROBLEMS, Pages 214-249 CHAPTER 11 - INTEGRAL EQUATION PERTURBATION METHODS, Pages 250-284 APPENDIX, Pages 285-289 BIBLIOGRAPHY, Pages 290-291 INDEX, Pages 293-296 Many physical problems that are usually solved by differential equation methods can be solved more effectively by integral equation methods. Such problems abound in applied mathematics, theoretical mechanics, and mathematical physics. The second edition of this widely used book continues the emphasis on applications and presents a variety of techniques with extensive examples. Additional material has been added throughout the book. The chapters dealing with differential equations and singular integral equations have been expanded considerably. Thus the book is ideal as a text for a beginning graduate level course. Its treatment of boundary value problems and an extended and up-to-date bibliography will also make the book useful to research workers in many applied fields. Intended for use on a beginning graduate-level course in the solution of problems using integral equation methods, this second edition presents a variety of techniques with extensive examples. Boundary value problems are emphasized, and there is an extended bibliography