Fourier Analysis and Its Applications
Seiten
2003
Springer-Verlag New York Inc.
978-0-387-00836-3 (ISBN)
Springer-Verlag New York Inc.
978-0-387-00836-3 (ISBN)
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.
Anders Vretblad is Senior Lecturer of Mathematics at Uppsala University, Sweden.
Introduction.- Preparations.- Laplace and Z Transforms.- Fourier Series.- L^2 Theory.- Separation of Variables.- Fourier Transforms.- Distributions.- Multi-Dimensional Fourier Analysis.- Appendix A: The ubiquitous convolution.- Appendix B: The Discrete Fourier Transform.- Appendix C: Formulae.- Appendix D: Answers to exercises.- Appendix E: Literature.
| Erscheint lt. Verlag | 4.1.2005 |
|---|---|
| Reihe/Serie | Graduate Texts in Mathematics ; 223 |
| Zusatzinfo | XII, 272 p. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Naturwissenschaften ► Physik / Astronomie | |
| ISBN-10 | 0-387-00836-5 / 0387008365 |
| ISBN-13 | 978-0-387-00836-3 / 9780387008363 |
| Zustand | Neuware |
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