Advanced mathematical methods 0800-PA-AMATH

Lectures and classes
I. Complex analysis
1) Cauchy-Riemann conditions,
2) Cauchy theorem,
3) Infinite complex series
4) residua and its applications,
5) contour integration,
II. Tensor calculus
1) tensor algebra,
2) exterior algebra
3) manifolds and tangent vectors,
4) tensor fields
5) tensor analysis: covariant derivative, parallel transport,
Lie derivative, Killing vectors, differential forms
6) Riemannian manifolds
III. Elements of group theory
1) introduction to discrete and continuous group,
2) basics of representation theory, Schur lemma, orthogonality conditions
3) basics of Lie group and Lie algebra theory.