640-356 Theoretical Methods for Physics

Mathematics 620-231 or 620-233; and mathematics 620-232 or 620-234; physics 640-223 or 640-243, and physics 640-225 or 640-245.

This subject covers a variety of techniques for solving a range of generic problems in physics. It underpins other physics subjects and is invaluable preparation for students considering further studies in physics.

Students completing this subject will be able to:

• explain how physics problems are formulated, analysed and solved using a wide range of theoretical methods; and

• solve problems by applying these methods to a wide range of physical situations.

In addition, students will enhance their ability to:

• participate effectively as part of a group in tutorials; and

• plan effective work schedules and manage their time to meet the deadlines for submission of assessable work and prepare for tests and examinations.

This subject provides an introduction to linear systems: time and frequency representation, natural modes of coupled systems, Fourier, Laplace, Mellin and Hankel transform techniques, stability and causality; symmetry in physical systems: group theory and physical applications - angular momentum, isospin, crystallography; potential theory for electrostatics, magnetostatics and gravitation in two and three dimensions: solution by functions of a complex variable, Bessel and Legendre functions, Green functions, integral equations; and waves and diffusion in one-, two- and three-dimensional continuous and discrete spaces: strings, lattices, drum skins, acoustics and heat conduction.

A 3-hour end-of-semester written examination; plus tests totalling up to two hours and/or projects and/or assignments totalling up to an equivalent of no more than 3000 words, set during the semester and which may account for up to 20% of the final mark.