640-356 Theoretical Methods for Physics

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Objectives:

This course will provide students with:

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

• an ability to apply these methods to a wide range of physical situations;

• a grounding in relevant theoretical methods for those with an experimental orientation.

Content:

A selection from:

Linear systems: signals and noise, time and frequency representation, linear response in electronics, natural modes of coupled systems, Fourier and Laplace transform techniques. Stability and causality.

Potential theory for electrostatics, magnetostatics and gravitation in 2 and 3 dimensions: solution by functions of a complex variable, Bessel and Legendre functions, Green functions.

Waves and diffusion in 1, 2 and 3 dimensional continuous and discrete spaces: strings, lattices, drum skins, acoustics and heat conduction, Fick's law.

Symmetry in physical systems: Cartesian tensors in elasticity, optics and electromagnetism. Notions of groups and group representations.

Assessment: