Graduate course: Classical Mechanics (2014 -- 2016)

Textbook: "Classical Mechanics", third edition, by Goldstein, Poole and Safko

Lecture notes:

1. Survey of elementary principles
2. Variational principles and Lagrange's equations
3. The central force problem
4. Kinematics of rigid body motion
5. Rigid body equation of motion
6. Oscillations
7. Special theory of relativity
8. The Hamilton equations of motion
9. Canonical transformations
10. Hamilton-Jacobi theory, action-angle variables
11. (skipped) clssical chaos
12. Canonical perturbation theory
13. Continuous systems and fields

Undergraduate course: Applied Mathematics IV (2015, 2016)

Textbook: "Mathematical Methods for Physics and Engineering", third edition

by K.F. Riley, M.P. Hobson and S.J. Bence, Cambridge University Press, Chapters 17, 18, 20, 21, 22, 28, 29

Extra lectures on Lie groups and Lie algebras

Lecture notes:

1. Eigenfunction methods for differential equations [01]
2. Special functions [02] [03] [04] [05]
3. Partial differential equations [06] [07] [08] [09]
4. Calculus of variations [10]
5. Group theory [11]
6. Group representation theory [12]
7. Lie groups and Lie algebras [13]