Math 412: Syllabus     Flow in 1D :   - fixed points and stability
                                                    - phase portraits
                                                    - bifurcations
                                                    - simple oscillators
                               Flow in 2D : Linear systems
                                                    - eigenvalues,eigenvectors and solutions
                                                    - phase portraits
                                                    - stability
                                                    - bifurcations
                                                  Nonlinear systems
                                                    - Linearization about fixed points
                                                    - nolinear phase portraits
                                                    - Limit cycles, Poincare-Bendixson Theorem
                                                    - bifurcations
                               Flow in 3D: Chaos
                                                    -Lorenz equations, the Lorenz attractor
                                                    -discrete maps: tent map, logistic map
                                                    -fractals: dimension of a set, sample fractals
                                                    -strange attractors
                               Periodic flows in nD : Poincare maps (time permitting)