Mathematical Methods of Physics

Mathematical methods of Physics is a book on common techniques of applied mathematics that are often used in theoretical physics. It may be accessible to anyone with beginning undergraduate training in mathematics and physics. It is hoped that the book will be useful for anyone wishing to study advanced Physics.

Foreword

Vector Calculus

• Vector Spaces
• Matrices
• Gradient, Curl and Divergence
• Gauss' Theorem
• Stokes' Theorem
• The Laplacian

Complex Variables

• Analytic functions
• Cauchy's integral formula
• Residue Theorem
• Contour integration

Fourier Analysis

• Fourier's theorem
• Fourier transforms
• Linear filters

Hilbert Spaces

• Linear Algebra
• Riesz representation theorem
• Operators

Green's Functions

• General theory
• Solutions of differential equations
• Applications to wave mechanics

Sturm-Liouville Theory

• Orthogonal functions
• Bessel, Legendre polynomials
• Special functions

Cartesian Tensors

• Coördinate transforms
• The multipole expansion
• Summation convention
• Special relativity