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Full Description
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.
Contents
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.
