Unique in its clarity, examples and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research. The author illustrates the mathematics with numerous physical examples drawn from contemporary research. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations and Bessel functions, this textbook covers topics such as the singular-value decomposition, Lie algebras, the tensors and forms of general relativity, the central limit theorem and Kolmogorov test of statistics, the Monte Carlo methods of experimental and theoretical physics, the renormalization group of condensed-matter physics and the functional derivatives and Feynman path integrals of quantum field theory.
Kevin Cahill is Professor of Physics and Astronomy at the University of New Mexico. He has done research at NIST, Saclay, Ecole Polytechnique, Orsay, Harvard University, NIH, LBL and SLAC, and has worked in quantum optics, quantum field theory, lattice gauge theory and biophysics. Physical Mathematics is based on courses taught by the author at the University of New Mexico and at Fudan University in Shanghai.
Preface; 1. Linear algebra; 2. Fourier series; 3. Fourier and Laplace transforms; 4. Infinite series; 5. Complex-variable theory; 6. Differential equations; 7. Integral equations; 8. Legendre functions; 9. Bessel functions; 10. Group theory; 11. Tensors and local symmetries; 12. Forms; 13. Probability and statistics; 14. Monte Carlo methods; 15. Functional derivatives; 16. Path integrals; 17. The renormalization group; 18. Chaos and fractals; 19. Strings; Index.