Fourier Analysis and Its Applications

Bild: 9781441918413 | Fourier Analysis and Its Applications | Anders Vretblad | Taschenbuch

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Beschreibung

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.

Über den Autor

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

Zusammenfassung

This book is a carefully prepared account of the basic ideas in
Fourier analysis and its applications to the study of partial
differential equations. The author succeeds to make his exposition
accessible to readers with a limited background, for example, those
not acquainted with the Lebesgue integral. Readers should be familiar
with calculus, linear algebra, and complex numbers. A variety of
worked examples and exercises will help the readers to apply their
newly acquired knowledge.

Inhaltsverzeichnis

Introduction * Preparations * Laplace and Z Transforms * Fourier Series * L^2 Theory * Separation of Variables * Fourier Transforms * Distributions * Multi-Dimentional Fourier Analysis * Appendix A: The ubiquitous convolution * Appendix B: The Discrete Fourier Transform * Appendix C: Formulae * Appendix D: Answers to exercises * Appendix E: Literature

Details

Erscheinungsjahr:	2010
Fachbereich:	Analysis
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xii 272 S.
ISBN-13:	9781441918413
ISBN-10:	1441918418
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Vretblad, Anders
Auflage:	Softcover reprint of the original 1st edition 2003
Hersteller:	Springer US Springer New York Springer US, New York, N.Y.
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 16 mm
Von/Mit:	Anders Vretblad
Erscheinungsdatum:	29.11.2010
Gewicht:	0,441 kg

Artikel-ID: 107253318

Über den Autor

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

Zusammenfassung

Inhaltsverzeichnis

Details

Erscheinungsjahr:	2010
Fachbereich:	Analysis
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xii 272 S.
ISBN-13:	9781441918413
ISBN-10:	1441918418
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Vretblad, Anders
Auflage:	Softcover reprint of the original 1st edition 2003
Hersteller:	Springer US Springer New York Springer US, New York, N.Y.
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 16 mm
Von/Mit:	Anders Vretblad
Erscheinungsdatum:	29.11.2010
Gewicht:	0,441 kg