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Full Description
This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern analysis to develop the concepts and reasoning behind the techniques without getting bogged down in the technicalities of rigorous proofs.
Contents
Preface
Contents
Chapter 1. Overture
Chapter 2. Fourier series
Chapter 3. Orthogonal sets of functions
Chapter 4. Some boundary value problems
Chapter 5. Bessel functions
Chapter 6. Orthogonal polynomials
Chapter 7. The Fourier transform
Chapter 8. The Laplace transform
Chapter 9. Generalized functions
Chapter 10. Green's functions
Appendices
Answers to the Exercises
References
Index of Symbols
Index
