# Unit information: Methods of Theoretical Physics 3 in 2019/20

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Unit name Methods of Theoretical Physics 3 PHYS30015 10 H/6 Teaching Block 2 (weeks 13 - 24) Dr. Gradhand Not open Level I/5 Mathematical Physics PHYS23020. None School of Physics Faculty of Science

## Description

This course introduces major mathematical methods of theoretical physics. The unit begins with briefly reviewing and expancing the material from previous maths for physics courses. The main content is the theory of complex functions of a complex variable, their differentiation and integration, including Cauchy's residue theorem and its applications for real integrals. The course describes the important theory of complex functions of complex variables, and then applies them to Green functions for the important partial differential equations of physics, so providing the foundations for advanced mathematical and theoretical physics topics in later years.

This unit is taken as an optional third year physics unit. It is similar to the second year unit PHYS20006 Methods of Theoretical Physics 2, but with some material and exam assessment specific to third year physics students.

## Intended learning outcomes

Students will be able to

• Determine whether a given function of a complex variable is analytic, and calculate and manipulate the Cauchy-Riemann equations
• Perform complex contour integrals and construct Taylor and Laurent series for complex functions
• Locate poles and perform integrals using Cauchy's theorem of residues
• Construct Green functions for simple ODEs, including identifying correct choice of integration contour
• Recognise and manipulate Green functions for the major PDEs of mathematical physics.

## Teaching details

18 lectures, 3 x two hour problems classes, self-study.

## Assessment Details

Formative: problem sheets for self-study throughout course; 3 x 2-hour problems classes.

Summative: 2-hour written exam (100%).