Plan

 MondayWednesdayThursday
Week 1Class start
Geometrical approach, population model
Sections 2.0-2.3		Population model cont'd, stability of fixed points
2.3-2.4
Week 2Linearization, Existence and Uniqueness
2.4-2.5		more ex phase portrait, Existence and Uniqueness
2.2, 2.5		Existence and Uniqueness cont'd, impossibility of oscillations, potentials
2.5-2.7
week 3Potentials cont'd, Bifurcation: saddle-node
3.0-3.1
Bifurcation: saddle-node cont'd
3.1		saddle-node cont'd
3.1
week 4transcritical bifurcation
3.2		transcritical bifurcation cont'd, Pitchfork Bifurcation, supercritical
3.2 , 3.4		Pitchfork Bifurcation, supercritical/subcritical
3.4
week 5Example Hysterisis cont'd
3.4		2D Linear systems
5.0, 5.1		2D Linear systems
5.1
week 6Reading weekReading weekReading week
week 72D Linear systems cont'd, stability, general case
5.1		2D Linear systems general case cont'd
5.2		2D Linear systems: general case cont'd
5.2
week 82D Linear systems cont'd, examples, classifications
5.2		2D Linear systems cont'd: classifications
5.2		Midterm
week 9Trace-Det plane, bifurcation, ex
Section 5.2		Nonlinear systems, existence and uniqueness, examples
Sections 6.1 and 6.2		Nonlinear systems ex cont'd, hyperbolic f.pts, Poincaré Stability Thm
Section 6.3
week 10Stability revisited, examples of the Poincaré stability thm, ex of nonhyperbolic f pt.
6.3		Example of nonlinear system and its phase portrait with the help of linearization
6.3		idea of the proof of Poincaré's linearization theorem.
6.3
week 11Hamiltonian systems
6.3, 6.5		Conservative systems
6.5		conservative systems, Nonlinear Pendulum
6.5
week 12Nonlinear Pendulum, Lyapunov Method
6.5, 7.2
6.7		Lyapunov method for stability, Gradient systems, limit cycles
7.2, 7.1		Limit cycles, Poincaré-Bendixson
7.1, 7.3
week 13Bifurcation revisited
8.1		Bifurcation cont'd
8.1, 8.2		Bifurcation cont'd
Hopf bifurcation,
8.1, 8.2
week 14Bifurcation cont'd
8.1, 8.2
Last day of class!