Fourier Analysis and Its Applications
-4 %

Fourier Analysis and Its Applications

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ISBN-13:
9780387008363
Erscheinungsdatum:
01.01.2005
Seiten:
272
Autor:
Anders Vretblad
Gewicht:
608 g
Format:
241x161x22 mm
Serie:
223, Graduate Texts in Mathematics
Sprache:
Englisch
Beschreibung:

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. At the same time, the author has managed to include 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 does not find in books at this level. A variety of worked examples and exercises will help the readers to apply their newly acquired knowledge.
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.
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

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