
Fourier Analysis and Its Applications
Gerald B. Folland(Author)
American Mathematical Society (Publisher)
Published on 28. February 2009
Book
Hardback
433 pages
978-0-8218-4790-9 (ISBN)
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.
Reviews / Votes
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
More details
Series
Language
English
Place of publication
Providence
United States
Target group
College/higher education
Illustrations
illustrations
Dimensions
Height: 257 mm
Width: 185 mm
Thickness: 28 mm
Weight
951 gr
ISBN-13
978-0-8218-4790-9 (9780821847909)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
Gerald B. Folland, University of Washington, Seattle, WA, USA
Content
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
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