Advanced Mathematical Methods 2
20 credits / 30 lectures
This course will introduce and develop a number of classical (and some not so classical) methods in mathematical physics, building on the third year courses on complex variables and mathematical physics.
Part 1. Advanced Complex Methods:
- 1.1. Integral representations and complex differential equations.
- 1.2. The hypergeometric equation and hypergeometric functions.
- 1.3. The hydrogen atom
Part 2. Advanced Greens Function Methods:
- 2.1. From integrals to path integrals
- 2.2. Lies, damn lies and statistical mechanics
- 2.3. Perturbation theory - size matters
- 2.4. Correlation functions - 1, 2, 3, many
- 2.5. Topology and integrals Part
3. Advanced other things:
- 3.1. Grassman variables - who ordered that?
- 3.2. Statistical systems in and out of equilibrium
- 3.3. The Ising on the cake - a 2-dimensional solvable system.