Physical Mathematics SECOND EDITION

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.

Kevin Cahill is Professor of Physics and Astronomy at the University of New Mexico. He has carried out research at the National Institute of Standards and Technology, Saclay, Ecole Polytechnique, Orsay, Harvard University, National Institutes of Health, Lawrence Berkeley National Laboratory and the SLAC National Accelerator Laboratory, and has worked in quantum optics, quantum field theory, lattice gauge theory and biophysics. This book is based on courses taught by the author at the University of New Mexico and at Fudan University in Shanghai.