Unit information: Methods of Theoretical Physics 2 in 2020/21

Unit name	Methods of Theoretical Physics 2
Unit code	PHYS20006
Credit points	10
Level of study	I/5
Teaching block(s)	Teaching Block 2 (weeks 13 - 24)
Unit director	Professor. Popescu
Open unit status	Not open
Pre-requisites	Level I/5 Mathematical Physics PHYS23020.
Co-requisites	None.
School/department	School of Physics
Faculty	Faculty of Science

Description including Unit Aims

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 Information

The unit will be taught through a combination of

• asynchronous online materials, including narrated presentations and worked examples
• synchronous group problems classes, workshops, tutorials and/or office hours
• asynchronous directed individual formative exercises and other exercises
• guided, structured reading

Assessment Information

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

Summative: 2-hour written timed, open-note examination(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