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Fourier Series /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2012.
|
| Colección: | Classroom resource materials.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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 dimensions1.2 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 series3.6 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