After some twenty years of teaching different topics in the Department of Mathematical Physics at the University of Adelaide I conceived the rather foolhardy project of putting all my undergraduate notes together in one single volume under the title Mathematical Physics. This undertaking turned out to be considerably more ambitious than I had originally expected, and it was not until my recent retirement that I found the time to complete it.

Over the years I have sometimes found myself in the midst of a vigorous and at times quite acrimonious debate on the difference between theoretical and mathematical physics. This book is symptomatic of the difference. I believe that mathematical physicists put the mathematics first, while for theoretical physicists it is the physics which is uppermost. The latter seek out those areas of mathematics for the use they may be put to, while the former have a more unified view of the two disciplines. I don't want to say one is better than the other – it is simply a different outlook. In the big scheme of things both have their place but, as this book no doubt demonstrates, my personal preference is to view mathematical physics as a branch of mathematics.

The classical texts on mathematical physics which I was originally brought up on, such as Morse and Feshbach [7], Courant and Hilbert [1], and Jeffreys and Jeffreys [6] are essentially books on differential equations and linear algebra. The flavour of the present book is quite different.