Methods of Mathematical Physics

This book is a reissue of classic textbook of mathematical methods.

Harold Jeffreys (Author), Bertha Jeffreys (Author)

9780521664028, Cambridge University Press

Paperback, published 18 November 1999

730 pages, 91 b/w illus. 252 exercises
22.8 x 15.3 x 4.4 cm, 1.138 kg

'This outstandingly excellent mathematical treatise … The work is a fine product of British mathematical scholarship, and a benefaction to the cause of progress in natural philosophy.' Nature

This well-known text and reference contains an account of those parts of mathematics that are most frequently needed in physics. As a working rule, it includes methods which have applications in at least two branches of physics. The authors have aimed at a high standard of rigour and have not accepted the often-quoted opinion that 'any argument is good enough if it is intended to be used by scientists'. At the same time, they have not attempted to achieve greater generality than is required for the physical applications: this often leads to considerable simplification of the mathematics. Particular attention is also paid to the conditions under which theorems hold. Examples of the practical use of the methods developed are given in the text: these are taken from a wide range of physics, including dynamics, hydrodynamics, elasticity, electromagnetism, heat conduction, wave motion and quantum theory. Exercises accompany each chapter.

1. The real variable
2. Scalars and vectors
3. Tensors
4. Matrices
5. Multiple integrals
6. Potential theory
7. Operational methods
8. Physical applications of the operational method
9. Numerical methods
10. Calculus of variations
11. Functions of a complex variable
12. Contour integration and Bromwich's integral
13. Contour integration
14. Fourier's theorem
15. The factorial and related functions
16. Solution of linear differential equations of the second order
17. Asymptotic expansions
18. The equations of potential, waves and heat conduction
19. Waves in one dimension and waves with spherical symmetry
20. Conduction of heat in one and three dimensions
21. Bessel functions
22. Applications of Bessel functions
23. The confluent hypergeometric function
24. Legendre functions and associated functions
25. Elliptic functions
Notes
Appendix on notation
Index.

Subject Areas: Maths for engineers [TBJ], Maths for scientists [PDE]