A Course of Modern Analysis

ISBN-13: 9781316518939 / Angielski / Twarda / 2021 / 700 str.

G. N. Watson

Opis

New edition of a true classic in mathematics. Preserves the flavour of the original, updating where appropriate and improving usability.

Recenzje

'In many cases the coverage here is still the best or one of the best available, and is concise and all in one volume.' Allen Stenger, Mathematical Association of America

Spis treści

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.