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Semester 1

Methods of Mathematical Physics (PHYS10034)

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Physics and Astronomy





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Course Summary

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.

Course Description

- 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

Assessment Information

Written Exam 100%, Coursework 0%, Practical Exam 0%

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