Mechanics, from Newtonian dynamics to Hamiltonian formulation
Classical mechanics, the foundation of the theory sequence. The course develops Newtonian mechanics (space and time, the postulates of dynamics, conservation laws, reference frames, the two-body problem, and oscillations), Lagrangian mechanics (constraints, the variational principle, the Euler–Lagrange equations, and Noether's theorem), the dynamics of rigid bodies (the inertia tensor and elements of the theory of the spinning top), and Hamiltonian mechanics (the Legendre transform, Hamilton's equations, phase space, Poisson brackets, canonical transformations, and Liouville's theorem), closing with deterministic chaos — examples of chaotic behaviour, linear stability theory, and the divide between integrability and non-integrability.