**Pure and Applied Undergraduate Texts**

Volume: 4;
1992;
433 pp;
Hardcover

MSC: Primary 42;
Secondary 00; 33; 34; 44; 46

Print ISBN: 978-0-8218-4790-9

Product Code: AMSTEXT/4

List Price: $76.00

Individual Member Price: $60.80

**Electronic ISBN: 978-1-4704-1117-6
Product Code: AMSTEXT/4.E**

List Price: $76.00

Individual Member Price: $60.80

#### Supplemental Materials

# Fourier Analysis and Its Applications

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*Gerald B. Folland*

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.

#### Table of Contents

# Table of Contents

## Fourier Analysis and Its Applications

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Preface v6 free
- Contents ix10 free
- 1 Overture 112 free
- 2 Fourier Series 1829
- 3 Orthogonal Sets of Functions 6273
- 4 Some Boundary Value Problems 97108
- 5 Bessel Functions 127138
- 6 Orthogonal Polynomials 164175
- 7 The Fourier Transform 204215
- 8 The Laplace Transform 256267
- 9 Generalized Functions 303314
- 10 Green's Functions 349360
- Appendices 386397
- Answers to the Exercises 413424
- References 426437
- Index of Symbols 429440 free
- Index 430441
- Back Cover Back Cover1445

#### Readership

Undergraduate and graduate students interested in studying the Fourier transform.

#### Reviews

The book is a detailed and very readable treatise on the theory and practice of series expansions and transforms. The primary audience consists of advanced undergraduates in mathematics, physics, and engineering, but the book is also a useful reference for more advanced workers . . . The strength of the book comes from its careful presentation of theory followed by detailed applications, with good illustrations, and finally a generous collection of exercises (with answers). The prose is smooth and gives understandable discussions of technical difficulties . . . This text can surely be recommended for use in a one or two semester course, or as a reference for graduate students or other persons who want to see what sort of problems Fourier analysis was invented to solve.

-- C. F. Dunkl, Zentralblatt MATH

With the same mastery as in his *Real analysis*, the author now offers
us this excellent textbook on Fourier analysis: Fourier series, orthogonal
systems, Bessel functions, Fourier and Laplace transforms, which are all very
powerful mathematical tools in many a scientific domain. Without being
exhaustive and without falling into a profusion of boring details, it
nevertheless gives a panorama of these topics that is as complete as the
framework of the book allows. Thus this text, which is designed for courses at
the advanced undergraduate level and beyond, will also serve as a useful
reference book.

-- Mathematical Reviews

- Overture
- Fourier series
- Orthogonal sets of functions
- Some boundary value problems
- Bessel functions
- Orthogonal polynomials
- The Fourier transform
- The Laplace transform
- Generalized functions
- Green's functions
- Appendices
- Answers to the exercises
- References
- Index of symbols
- Index