Physical Mathematics

With examples drawn from contemporary physics this book clearly explains the mathematics graduate students need to succeed in their courses.

Kevin Cahill (Author)

9781108470032, Cambridge University Press

Hardback, published 15 August 2019

778 pages, 71 b/w illus. 465 exercises
25.2 x 17.8 x 3.9 cm, 1.68 kg

'The book places itself as a reference for the undergraduate students, the graduate students and the researchers who need to refresh some topics. As the author indicates, the book covers all the mathematics needed for a physicist. Also, the instructor who gives a course on mathematical physics can find useful material in the book. The topics are explained with little stress on the physical meaning which is meant to come spontaneously progressing in the book. The completeness of topics is preferred to proofs and deep explanations … this book is indicated for the student who wants a solid and complete reference for mathematical tool in physics. The instructor can use the book as a reference for basic or advanced courses of mathematical physics, as well as for more theoretically based courses.' Stefano Scali, Contemporary Physics

Unique in its clarity, examples, and range, Physical Mathematics explains simply and succinctly the mathematics that graduate students and professional physicists need to succeed in their courses and research. The book illustrates the mathematics with numerous physical examples drawn from contemporary research. This second edition has new chapters on vector calculus, special relativity and artificial intelligence and many new sections and examples. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations, Bessel functions, and spherical harmonics, the book explains topics such as the singular value decomposition, Lie algebras and group theory, tensors and general relativity, the central limit theorem and Kolmogorov's theorems, Monte Carlo methods of experimental and theoretical physics, Feynman's path integrals, and the standard model of cosmology.

Preface
1. Linear algebra
2. Vector calculus
3. Fourier series
4. Fourier and Laplace transforms
5. Infinite series
6. Complex-variable theory
7. Differential equations
8. Integral equations
9. Legendre polynomials and spherical harmonics
10. Bessel functions
11. Group theory
12. Special relativity
13. Tensors and general relativity
14. Forms
15. Probability and statistics
16. Monte Carlo methods
17. Artificial intelligence
18. Order, chaos, and fractals
19. Functional derivatives
20. Path integrals
21. Renormalization group
22. Strings
References
Index.

Subject Areas: Mathematical modelling [PBWH]