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, <em>Zentralblatt MATH</em><br /><br />"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." - <em>Mathematical Reviews</em>

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.
Read more
Presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. This title includes material on Bessel functions, orthogonal polynomials, and Laplace transforms.
Read more
  • 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
Read more

Product details

ISBN
9780821847909
Published
2009-02-28
Publisher
American Mathematical Society
Weight
951 gr
Height
257 mm
Width
185 mm
Thickness
28 mm
Age
UU, UP, 05
Language
Product language
Engelsk
Format
Product format
Innbundet
Number of pages
433

Biographical note

Gerald B. Folland, University of Washington, Seattle, WA, USA