Course Syllabus

Tenative Course Schedule

1Motivating Examples, Linear Systems, Examples and ClassificationStrogatz Chapter 1, 5.0-5.3HW 1 Assigned
2Phase Plane: Phase PortraitsStrogatz 6.0-6.4HW 2 Assigned; HW 1 Due
3Fixed Points and Linearization, Potentials, Conservative Systems, Reversible SystemsStrogatz 2.7, 6.5-6.8HW 3 Assigned; HW 2 Due
4Pendulum Example, Index Theory; Nonlinear Stability Theory: Lyapunov StabilityStrogatz 6.7, 6.8; Perko Chapter 3HW 4 Assigned; HW 3 Due
5Limit Cycles: Examples, Ruling Out Closed Orbits; Poincare BendixsonStrogatz 7.0-7.3Midterms Week
6Lienard Systems, Relaxation Oscillations, Weakly Nonlinear OscillatorsStrogatz 7.4-7.6HW 5 Assigned; HW 4 Due
7Weakly Nonlinear Oscillators; Bifurcations: Saddle-Node BifurcationsStrogatz 7.6, 3.0-3.1HW 6 Assigned; HW 5 Due
8Transcritical Bifurcations, Pitchfork Bifurcations, 2D Bifurcations: Saddle-Node, Transcritical and PitchforkStrogatz 3.2, 3.4, 8.0,8.1HW 7 Assigned; HW 6 Due
9Hopf Bifucations and Examples; Review/Guest LectureStrogatz 8.2HW 7 Due
10Finals Week