E. T. Whittaker

Course of Modern Analysis (eBook, PDF)

• Format: PDF

Produktbeschreibung

This classic work has been a unique resource for thousands of mathematicians, scientists and engineers since its first appearance in 1902. Never out of print, its continuing value lies in its thorough and exhaustive treatment of special functions of mathematical physics and the analysis of differential equations from which they emerge. The book also is of historical value as it was the first book in English to introduce the then modern methods of complex analysis. This fifth edition preserves the style and content of the original, but it has been supplemented with more recent results and references where appropriate. All the formulas have been checked and many corrections made. A complete bibliographical search has been conducted to present the references in modern form for ease of use. A new foreword by Professor S.J. Patterson sketches the circumstances of the book's genesis and explains the reasons for its longevity. A welcome addition to any mathematician's bookshelf, this will allow a whole new generation to experience the beauty contained in this text.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 26. August 2021
• Englisch
• ISBN-13: 9781009008594
• Artikelnr.: 66176053

Autorenporträt

E. T. Whittaker was Professor of Mathematics at the University of Edinburgh. He was awarded the Copley Medal in 1954, 'for his distinguished contributions to both pure and applied mathematics and to theoretical physics'.

Inhaltsangabe

Foreword S. J. Patterson
Introduction
Part I. The Process of Analysis: 1. Complex numbers
2. The theory of convergence
3. Continuous functions and uniform convergence
4. The theory of Riemann integration
5. The fundamental properties of analytic functions - Taylor's, Laurent's and Liouville's theorems
6. The theory of residues - application to the evaluation of definite integrals
7. The expansion of functions in infinite series
8. Asymptotic expansions and summable series
9. Fourier series and trigonometric series
10. Linear differential equations
11. Integral equations
Part II. The Transcendental Functions: 12. The Gamma-function
13. The zeta-function of Riemann
14. The hypergeometric function
15. Legendre functions
16. The confluent hypergeometric function
17. Bessel functions
18. The equations of mathematical physics
19. Mathieu functions
20. Elliptic functions. General theorems and the Weierstrassian functions
21. The theta-functions
22. The Jacobian elliptic functions
23. Ellipsoidal harmonics and Lamé's equation
Appendix. The elementary transcendental functions
References
Author index
Subject index.