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Fourier Series

Author: Rajendra Bhatia
Publisher: Cambridge : Cambridge University Press, 2012.
Series: Classroom resource materials.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Bhatia, Rajendra.
Fourier Series.
Washington : Mathematical Association of America, ©2014
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Rajendra Bhatia
ISBN: 9781614441045 1614441049
OCLC Number: 889953111
Notes: Title from publishers bibliographic system (viewed on 11 Apr 2014).
Description: 1 online resource.
Contents: ""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 Cesà ro 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""
Series Title: Classroom resource materials.
Responsibility: Rajendra Bhatia.

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