The course is split into two halves. The first half focuses on nonlinear dynamics and the Lagrange and Hamilton formulation of mechanics, with topics including bifurcation theory, chaos, limit cycles, Noether's theorem, Lagrange multipliers, Poisson brackets and phase space orbits. The second half is dedicated to advanced electrodynamics and includes an introduction to co-variance, contra-variance, and index notation, vector calculus in various coordinate systems, the Lorentz transformation and special relativity, the transformation rules of electric and magnetic fields, the fields and potentials of relativistic charges, radiation, and the formulation of electromagnetism in terms of four-vectors and tensors.