Fourier Analysis and Its Applications (Graduate Texts in Mathematics, Vol. 223) - Hardcover

Vretblad, Anders

Hardcover

ISBN 10: 0387008365 ISBN 13: 9780387008363

Publisher: Springer, 2003

Synopsis

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.

About this title

About the Author

 Anders Vretblad is Senior Lecturer of Mathematics at Uppsala University, Sweden.

From the Back Cover

 This book presents the basic ideas in Fourier analysis and its applications to the study of partial differential equations. It also covers the Laplace and Zeta transformations and the fundaments of their applications. The author has intended to make his exposition accessible to readers with a limited background, for example, those not acquainted with the Lebesgue integral or with analytic functions of a complex variable. At the same time, he has included discussions of more advanced topics such as the Gibbs phenomenon, distributions, Sturm-Liouville theory, Cesaro summability and multi-dimensional Fourier analysis, topics which one usually will not find in books at this level.

Many of the chapters end with a summary of their contents, as well as a short historical note. The text contains a great number of examples, as well as more than 350 exercises. In addition, one of the appendices is a collection of the formulas needed to solve problems in the field.

Anders Vretblad is Senior Lecturer of Mathematics at Uppsala University, Sweden.

Edition details

• Publisher: Springer
• Publication date: 2003
• Language: English
• ISBN 10: 0387008365
• ISBN 13: 9780387008363
• Binding: Hardcover
• Edition number: 1
• Number of pages: 284