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Fourier Analysis and Its Applications

 Buch
Besorgungstitel | Lieferzeit:3-5 Tage I
ISBN-13:
9780387008363
Einband:
Buch
Seiten:
272
Autor:
A. Vretblad
Gewicht:
586 g
Format:
244x156x22 mm
Serie:
Vol.223, Graduate Texts in Mathematics
Sprache:
Englisch
Beschreibung:

From the contents:Introduction.- Preparations.- Laplace and Z Transforms.- Fourier Series.- L2 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.
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.

From the contents:Introduction.- Preparations.- Laplace and Z Transforms.- Fourier Series.- L2 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.
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.
Autor: A. Vretblad
Anders Vretblad is Senior Lecturer of Mathematics at Uppsala University, Sweden.
Autor: A. Vretblad
ISBN-13:: 9780387008363
ISBN: 0387008365
Verlag: Springer, Berlin
Gewicht: 586g
Seiten: 272
Sprache: Englisch
Sonstiges: Buch, 244x156x22 mm, w. 24 figs.