MAE5790-1 Course introduction and overview
1:16:31MAE5790-2 One dimensional Systems
1:16:44MAE5790-3 Overdamped bead on a rotating hoop
1:13:12MAE5790-4 Model of an insect outbreak
1:15:16MAE5790-5 Two dimensional linear systems
1:15:20MAE5790-6 Two dimensional nonlinear systems fixed points
1:07:17MAE5790-7 Conservative Systems
1:17:13MAE5790-8 Index theory and introduction to limit cycles
1:13:55Lecture 9: Testing for Closed Orbits (MAE 5790)
1:16:52Lecture 10: Van der Pol Oscillator (MAE 5790)
1:05:58Lecture 11: Averaging Theory for Weakly Nonlinear Oscillators (MAE 5790)
1:16:08Lecture 12: Bifurcations in Two-Dimensional Systems (MAE 5790)
46:54Lecture 13: Hopf Bifurcations in Aeroelastic Instabilities and Chemical Oscillators (MAE 5790)
1:07:57Lecture 14: Global Bifurcations of Cycles (MAE 5790)
1:16:23Lecture 15: Chaotic Waterwheel (MAE 5790)
1:14:12Lecture 16: Waterwheel Equations and Lorenz Equations (MAE 5790)
1:12:42Lecture 17: Chaos in the Lorenz Equations (MAE 5790)
1:16:36Lecture 18: Strange Attractor for the Lorenz Equations (MAE 5790)
1:13:48Lecture 19: One-Dimensional Maps (MAE 5790)
1:14:35Lecture 20: Universal Aspects of Period Doubling (MAE 5790)
1:11:56Lecture 21: Feigenbaum's Renormalization Analysis of Period Doubling (MAE 5790)
1:15:59Lecture 22: Renormalization: Function Space and a Hands-On Calculation (MAE 5790)
1:08:32MAE5790-5 Two dimensional linear systems
Jacob Gould Schurman Professor of Applied Mathematics
Phase plane analysis. Eigenvectors and eigenvalues. Classification of 2-D linear systems. Saddle points. Stable and unstable nodes and spirals. Centers. Non-isolated fixed points.
Reading: Strogatz, "Nonlinear Dynamics and Chaos", Chapter 5 and Sections 6.0--6.2.
MAE5790-4 Model of an insect outbreak
Next · Lecture 6MAE5790-6 Two dimensional nonlinear systems fixed points
Seminar notes & discussion
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