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# Unit information: Methods of Theoretical Physics 2 in 2016/17

Please note: you are viewing unit and programme information for a past academic year. Please see the current academic year for up to date information.

Unit name Methods of Theoretical Physics 2 PHYS20006 10 I/5 Teaching Block 2 (weeks 13 - 24) Professor. Goldstein 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 expanding 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 and propagators, so providing the foundations for advanced mathematical and theoretical physics topics in later years.

This unit is similar to the third year unit PHYS38014 Methods of Theoretical Physics 3, but with some material and some exam assessment specific to second year Theoretical 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%).

## Reading and References

M R Dennis et al, Mathematical Handbook for Bristol Theoretical Physics

M L Boas, Mathematical Methods in the Physical Sciences

G B Arfken, H J Weber, F E Harris, Mathematical Methods for Physicists