Fourier Analysis and Its Applications

By: Anders Vretblad

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Paperback | 29 November 2010

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288 Pages

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TheclassicaltheoryofFourierseriesandintegrals,aswellasLaplacetra- forms, is of great importance for physical and technical applications, and its mathematical beauty makes it an interesting study for pure mathema- cians as well. I have taught courses on these subjects for decades to civil engineeringstudents,andalsomathematicsmajors,andthepresentvolume can be regarded as my collected experiences from this work. There is, of course, an unsurpassable book on Fourier analysis, the tr- tise by Katznelson from 1970. That book is, however, aimed at mathem- ically very mature students and can hardly be used in engineering courses. Ontheotherendofthescale,thereareanumberofmore-or-lesscookbo- styled books, where the emphasis is almost entirely on applications. I have felt the need for an alternative in between these extremes: a text for the ambitious and interested student, who on the other hand does not aspire to become an expert in the ?eld. There do exist a few texts that ful?ll these requirements (see the literature list at the end of the book), but they do not include all the topics I like to cover in my courses, such as Laplace transforms and the simplest facts about distributions.

Industry Reviews

From the reviews:

"This book is one in the Graduate Texts in Mathematics series published by Springer. ... There is a variety of worked examples as well as 350-plus exercises ... . The book is a valuable addition to the literature on Fourier analysis. It is written with more mathematical rigour than many texts ... without being totally opaque to the non-specialist. ... The examples at the end of each chapter are well structured and a reader working through most of them will achieve a good understanding of the topics." (Graham Brindley, The Mathematical Gazette, Vol. 90 (517), 2006)

"The author ... presents the results of his experiences and choices for decades of teaching courses. ... The tables and formulas collected ... are of great service. At the end of each chapter there is a summary section that discusses the results, gives some history, and suggests instructive exercises. We thus have a solid course on Fourier analysis and its applications interesting for students and specialists in engineering as well as for mathematicians. ... I believe that the book will find numerous interested readers." (Elijah Liflyand, Zentralblatt MATH, Vol. 1032 (7), 2004)

"This book is an interesting mixture of a traditional approach ... and a more modern one, emphasizing the role of (tempered) distributions and the application aspects of Fourier analysis. ... The book is certainly highly recommendable for those who want to learn the essence of Fourier analysis in a mathematically correct way without having to go through too much technical details." (H.G. Feichtinger, Monatshefte fuer Mathematik, Vol. 143 (2), 2004)

"The book is appropriate for an advanced undergraduate or a master's level one-term introductory course on Fourier series with applications to boundary value problems. ... a deep idea is presented in a non-rigorous way both to show the usefulness of the idea and to stimulate interest in further study. ... The book has a goodcollection of exercises ... . Each chapter ends with both a summary of its main results and methods and historical notes." (Colin C. Graham, Mathematical Reviews, Issue 2004 e)

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