This course introduces some of the mathematical techniques that are frequently used
in the analysis of a variety of physical processes. These notes are a slightly expanded
version of a one-semester course that I gave at Case Western Reserve University in the
Fall of 1999. Although I chose several textbooks to accompany the course, much of the
material is presented in the way that I was taught it. I learnt mathematical physics
from many people at Cambridge University, but those whose lectures clearly influenced
these notes are Alan Macfarlane, Stephen Siklos, and John Stewart. In places I have
borrowed heavily from their presentations and so these notes are certainly not a wholly
original effort. However, I have tried to synthesize the material in a useful and orderly
way, and have contributed significant material where I felt that more clarity was needed.
It is my hope that these notes will evolve into a better and better resource as time
passes. Certainly there is much room for improvement, and I welcome comments and
suggestions from anyone who reads them.