Basics of Mathematical Tools for Physics

Notes on special functions, differential equations, linear algebra and a host of other math topics .  The wonderful art we call mathematics probably had its birth in explanations of the physical world. As this art has developed, it has informed our understanding of the physical world and even opened views to the world that were not avialable on the basis of experience alone. Today, we have a huge array of mathematical techniques of analysis that we can use to study the physical world around us. The purpose of this tutorial is serve as my personal notes taken during the study of these mathematical tools specifically applied to physics. I hope you enjoy the descriptions of analytical methods I provide here and invite your criticism to improve my own understanding as well as the value of this work. Throughout these pages, the techniques described will be those that provide a way to understand our observations of the physical world. Have fun.

Coordinate Systems and Transformations

Numbers

Algebra

Geometry

Trigonometry

Functions

Vector Analysis

Calculus

Differentiation

Integration

Differential Equations

Ordinary Diff EQ

Partial Diff EQ

Tensors

Linear Algebra

Series

Complex Functions

Fourier Analysis

Orthogonal Functions

Special Functions

Gamma Function

Bessel Functions

Legendre Functions

Hermite Functions

Laguerre Functions

Chebyshev Polynomials

Hypergeometric Functions

Integral Transforms

Integral Equations

Green's Functions

Calculus of Variations

Approximation Methods