**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.

## 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
- Reisz 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