These notes are taken by a student in a class. They are not edited and I am providing them in order to give you an idea of what is going on in the class.
Lecture 1: Course mechanics; Introduction to nonlinear systems
Lecture 2: Range of nonlinear phenomena
Lecture 3: Fold and transcritical bifurcations
Lecture 4: Pitchfork bifurcations; Phase portraits of 2nd order linear systems
Lecture 5: Phase portraits of nonlinear systems near hyperbolic equilibria (Hartman-Grobman); Bendixon's theorem
Lecture 6: Invariant sets; Poincare-Bendixon theorem; Hopf bifurcations
Lecture 7: Dimensional analysis and scaling; Center manifold theory
Lecture 8: Existence and uniqueness of solutions; Lipschitz continuity; Continuous dependence on initial conditions and parameters
Lecture 9: Effect of parameter variations on solutions; Sensitivity equations; Lyapunov stability
Lecture 10: Lyapunov's direct method