Methods of Mathematical Physics (PHYS10034)
Physics and Astronomy
Normal Year Taken
Delivery Session Year
A course on advanced methods of mathematical physics. The course aims to demonstrate the utility and limitations of a variety of powerful calculational techniques and to provide a deeper understanding of the mathematics underpinning theoretical physics. The course will review and develop the theory of: complex analysis and applications to special functions; asymptotic expansions; ordinary and partial differential equations, in particular, characteristics, integral transform and Green function techniques; Dirac delta and generalised functions; Sturm-Liouville theory. The generality of approaches will be emphasised and illustrative examples from electrodynamics, quantum and statistical mechanics will be given.
- Revision of infinite series; asymptotic series- Complex analysis: revision, residues and analytical continuation- Gamma function- Laplace and stationary phase methods; saddle point approximation- Dirac's delta function- Ordinary differential equations (ODEs): Green functions and solution via series- Special functions- Fourier transformations: definition, properties and application to ODEs- Laplace transforms: definition, properties and application to ODEs- Partial differential equations: characterisation and solution via Laplace and Fourier transforms- Examples: the wave equation, the diffusion equation and Laplace equation
Written Exam 100%, Coursework 0%, Practical Exam 0%
All course information obtained from this visiting student course finder should be regarded as provisional. We cannot guarantee that places will be available for any particular course. For more information, please see the visiting student disclaimer: