Course

Maxwell's theory: charge conservation, Maxwell's triumph, potentials, wave equations

Operations on distributions, Applications of distributions

Constraints, Vibrations of string: from discrete to continuum

Distributions, Test functions

Integrable systems, Hidden symmetries, Laplace-Runge-Lenz vector

SU(2) and SU(3) tensors, Young's tableau. 

Hamiltonian vector flows, Hamilton's function, Liouville's theorem, Hamilton-Jacobi equation

Killing metric, Coset manifold, Representation theory of SU(2) Lie algebra, SU(2) tensors.

Hamilton's equations, Poisson brackets, Canonical transformations

Examples of Lie groups continued: SO(m,n), SU(n), Cartan subalgebra, proof of irreducibility of the adjoint representation for simple Lie groups.

Euler-Lagrange equations, Integrals of motion, Noether's theorem

Lie algebras from Lie groups. The adjoint representation. Examples of Lie groups: GL(n,K), SO(n).