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.
Inhaltsverzeichnis
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.
