Basic facts about nonlinear systems; stability and near-equilibrium dynamics; bifurcations; dynamical systems on the plane; non-autonomous dynamical systems; chaotic dynamics.

Contents: calculus of variations: brachistochrone, Euler differential equations, natural and free boundary conditions, transversality, Hamilton's principle. - Lagrangian dynamics: virtual work, perfect constraints, principle of d'Alembert Lagrange, Lagrange II, equilibria, linearization. - approximation of dynamic continua: finite differences, weighted residuals, Ritz and Galerkin method.