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Home > MAM4001W > Applied Mathematics Modules > Advanced Mathematical Methods 2

Advanced Mathematical Methods 2

Associate Professor Jeff Murugan
2nd semester 2019
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.