*These notes originate from my half of our second-year mathematical physics lecture. I no longer teach this
module, so local students may wish to consult Edwin Flikkema's and Maire Gorman's notes in the first instance.
However, I like to think these pages may be helpful in perhaps giving another angle on the same material, so
I've decided to leave them online.*

Officially branded "Mathematical Physics", which is slightly misleading, this lecture and workshop module builds on the introductory Maths modules in Year-1 of both the Physics and Maths degree schemes. The aim is to introduce physicists to some of the slightly more complex mathematical concepts needed when doing physics at a professional level and to show mathematicians some applications of their trade. The module comprises two lectures and a two-hour workshop each week.

- Classification of differential equations
- Review of ordinary differential equations (ODEs)
- Finding physical boundary conditions
- Partial differential equations (PDEs) in physics
- The del operator
- Laplace's equation 1 - separation of variables
- ODE with constant coefficients
- Laplace's equation 2 - applying boundary conditions
- Fourier series
- Laplace's equation 3 - Fourier expansion
- Diffusion equation
- Wave equation 1 - general solution
- Wave equation 2 - two sets of boundary conditions
- Fourier transformation 1 - introduction
- Fourier transformation 2 - Fourier theorems
- Fourier transformation 3 - transforming in practice

These notes are meant to help you revise. However, I may include additional material in the lectures or not cover all of the material listed here.

- Ordinary differential equations and solution sheet
- Higher-order ODE and separating PDE and solution sheet
- Laplace and diffusion equations, series expansion and solution sheet
- Wave equation and solution sheet
- Fourier transforms and solution sheet

We recommend you use the solution sheets *after* having a go at the problems and discussing
them with fellow students and staff during the workshop.
There is also a toolbox sheet for revision.

I find Mary L Boas's book, *Mathematical Methods in the Physical Sciences*,
New York: Wiley, ^{2}1983 very useful. Many of the examples used in the workshops are based on
it. There are a few copies of various vintages in the Physical Sciences Library.