A course of modern analysis : an introduction to the general theory of infinite processes and of analytic functions with an account of the principal transcendental functions
Author(s)
Bibliographic Information
A course of modern analysis : an introduction to the general theory of infinite processes and of analytic functions with an account of the principal transcendental functions
Cambridge University Press, 2021
5th ed
- : hbk
Available at 17 libraries
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
: hbk.WHI||6||2(5)200043152260
-
The Institute for Solid State Physics Library. The University of Tokyo.図書室
: hbk.413.1:C1e7210397498
Note
Includes bibliographical references (p. 625-647) and index
Description and Table of Contents
Description
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.
Table of Contents
- 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 Lame's equation
- Appendix. The elementary transcendental functions
- References
- Author index
- Subject index.
by "Nielsen BookData"