First and Second Terms (Same as ME 232A and ME 232B) Content Analysis of models described by nonlinear differential equations. Topics: equilibria, stability, Lyapunov functions, periodic solutions, Poincaré Bendixon theory, Poincaré maps, attractors and structural stability, the Euler-Lagrange equations, mechanical systems, small oscillations, dissipation, energy as a Lyapunov function, conservation laws, introduction to simple bifurcations and eigenvalue crossing conditions, Discussion of bifurcations in applications, invariant manifolds, the method of averaging, Melnikov’s method and the Smale horseshoe.