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
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