Group Theory and Differential Equations

Part 1 Group theory: Galiliean group and group properties; extensions and foliations of groups; the proper rotation subgroup, SO(3); homomorphism between SO(3) and SU(2); reflections and the orthogonal group, O(3). Part 2 Lie algebra and manifolds: introduction to Lie algebras and manifolds; generation of Lie algebras from Lie groups; the adjoint space. Part 3 Differential forms and their applications: differential forms; classical dynamics; electrodynamics; generalized Stokes theorem. Part 4 Lie groups and differential equations: Lie group analysis of differential equations; Lie's first theorem - differential equations and group action; conformal group, its nonlinear action and its associated differential equations; conformal symmetry and space-time; group representation theory and related algebras.