Fourier Analysis and Boundary Value Problems

Author: Gonzalez-Velasco   Enrique A.  

Publisher: Elsevier Science‎

Publication year: 1996

E-ISBN: 9780080531939

P-ISBN(Paperback): 9780122896408

P-ISBN(Hardback):  9780122896408

Subject: O174.2 classical harmonic analysis (Fourier analysis)

Language: ENG

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Description

Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.

A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.

  • Topics are covered from a historical perspective with biographical information on key contributors to the field
  • The text contains more than 500 exercises
  • Includes practical applications of the equations to problems in both engineering and physics

Chapter

Front Cover

pp.:  1 – 4

Copyright Page

pp.:  5 – 6

Table of Contents

pp.:  6 – 10

Preface

pp.:  10 – 14

CHAPTER 1. A HEATED DISCUSSION

pp.:  14 – 36

CHAPTER 2. FOURIER SERIES

pp.:  36 – 97

CHAPTER 3. RETURN TO THE HEATED BAR

pp.:  97 – 146

CHAPTER 4. GENERALIZED FOURIER SERIES

pp.:  146 – 178

CHAPTER 5. THE WAVE EQUATION

pp.:  178 – 220

CHAPTER 6. ORTHOGONAL SYSTEMS

pp.:  220 – 250

CHAPTER 7. FOURIER TRANSFORMS

pp.:  250 – 279

CHAPTER 8. LAPLACE TRANSFORMS

pp.:  279 – 315

CHAPTER 9. BOUNDARY VALUE PROBLEMS IN HIGHER DIMENSIONS

pp.:  315 – 364

CHAPTER 10. BOUNDARY VALUE PROBLEMS WITH CIRCULAR SYMMETRY

pp.:  364 – 423

CHAPTER 11. BOUNDARY VALUE PROBLEMS WITH SPHERICAL SYMMETRY

pp.:  423 – 464

CHAPTER 12. DISTRIBUTIONS AND GREEN'S FUNCTIONS

pp.:  464 – 519

APPENDIX A. UNIFORM CONVERGENCE

pp.:  519 – 531

APPENDIX B. IMPROPER INTEGRALS

pp.:  531 – 548

APPENDIX C. TABLES OF FOURIER AND LAPLACE TRANSFORMS

pp.:  548 – 552

APPENDIX D. HISTORICAL BIBLIOGRAPHY

pp.:  552 – 556

Index

pp.:  556 – 566

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