Physical Mathematics

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.

Table of Contents

Chapter 1 Linear algebra
Chapter 2 Fourier series
Chapter 3 Fourier and Laplace transforms
Chapter 4 Infinite series
Chapter 5 Complex-variable theory
Chapter 6 Differential equations
Chapter 7 Integral equations
Chapter 8 Legendre functions
Chapter 9 Bessel functions
Chapter 10 Group theory
Chapter 11 Tensors and local symmetries
Chapter 12 Forms
Chapter 13 Probability and statistics
Chapter 14 Monte Carlo methods
Chapter 15 Functional derivatives
Chapter 16 Path integrals
Chapter 17 The renormalization group
Chapter 18 Chaos and fractals
Chapter 19 Strings