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008			240724s2005 xx o ||||0 eng d
020			_a9781614441045 _q(electronic bk.)
020			_z9780883857403
035			_a(MiAaPQ)EBC3330342
035			_a(Au-PeEL)EBL3330342
035			_a(CaPaEBR)ebr10722453
035			_a(OCoLC)929120413
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA404.B48 2005eb
082	0		_a515.2433
100	1		_aBhatia, Rejendra.
245	1	0	_aFourier Series.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2005.
264		4	_c©2007.
300			_a1 online resource (131 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
505	0		_aIntro -- copyright page -- title page -- Contents -- Preface -- 0 A History of Fourier Series -- 1. The motion of a vibrating string -- 2. J. D'Alembert -- 3. L. Euler -- 4. D. Bernoulli -- 5. J. Fourier -- 6. P. Dirichlet -- 7. B. Riemann -- 8. P. du Bois-Reymond -- 9. G. Cantor -- 10. L. Fejér -- 11. H. Lebesgue -- 12. A.N. Kolmogorov -- 13. L. Carleson -- 14. The L_2 theory and Hilbert spaces -- 15. Some modern developments-I -- 16. Some modern developments-II -- 17. Pure and applied mathematics -- Chapt 1 Heat Conduction and Fourier Series -- 1.1 The Laplace equation in two dimensions -- 1.2 Solutions of the Laplace equation -- 1.3 The complete solution of the Laplace equation -- 2 Convergence of Fourier Series -- 2.1 Abel summability and Cesàro summability -- 2.2 The Dirichlet and the Fejér kernels -- 2.3 Pointwise convergence of Fourier series -- 2.4 Term by term integration and differentiation -- 2.5 Divergence of Fourier series -- 3 Odds and Ends -- 3.1 Sine and cosine series -- 3.2 Functions with arbitrary periods -- 3.3 Some simple examples -- 3.4 Infinite products -- 3.5 π and infinite series -- 3.6 Bernoulli numbers -- 3.7 sinx/x -- 3.8 The Gibbs phenomenon -- 3.9 Exercises -- 3.10 A historical digression -- 4 Convergence in L_2 and L_1 -- 4.1 L_2 convergence of Fourier series -- 4.2 Fourier coefficients of L_1 functions -- 5 Some Applications -- 5.1 An ergodic theorem and number theory -- 5.2 The isoperimetric problem -- 5.3 The vibrating string -- 5.4 Band matrices -- A A Note on Normalisation -- B A Brief Bibliography -- Analysis -- Fourier series -- General reading -- History and biography -- Index -- Notation -- About the Author.
520			_aThis is a concise introduction to Fourier series covering history, major themes, theorems, examples and applications. It can be used to learn the subject, and also to supplement, enhance and embellish undergraduate courses on mathematical analysis.The book begins with a brief summary of the rich history of Fourier series over three centuries. The subject is presented in a way that enables the reader to appreciate how a mathematical theory develops in stages from a practical problem (such as conduction of heat) to an abstract theory dealing with concepts such as sets, functions, infinity and convergence. The abstract theory then provides unforeseen applications in diverse areas.The author starts out with a description of the problem that led Fourier to introduce his famous series. The mathematical problems this leads to are then discussed rigorously. Examples, exercises and directions for further reading and research are provided, along with a chapter that provides materials at a more advanced level suitable for graduate students. The author demonstrates applications of the theory to a broad range of problems.The exercises of varying levels of difficulty that are scattered throughout the book will help readers test their understanding of the material.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aFourier series.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aBhatia, Rejendra _tFourier Series _dProvidence : American Mathematical Society,c2005 _z9780883857403
797	2		_aProQuest (Firm)
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3330342 _zClick to View
999			_c79799 _d79799