Lecture plan
The plan may be changed. Probably I will try be a little bit a head of the this plan.
| Week | Topic | Sections | Home work | Remarks |
|---|---|---|---|---|
| 2 | Introduction Qualitative methods - the phase plane for 2x2 systems Existence and uniqueness of ODEs | J-S chp. 1 HO chp. 1 (J-S App. A) | Read yourself: J-S chp. 1 |
|
| 3 | Existence and uniqueness of ODEs (cont.) Phase plane for n×n systems | HO chp. 1 (J-S App. A) J-S chp. 2 | 1 | |
| 4 | Linearization of 2×2 systems - ideas Solution of linear 2x2 systems | J-S chp 2 HO chp. 2 | 2 | Read yourself: J-S chp. 2.2 |
| 5 | Phase plane for linear 2×2 systems Phase plane for general 2×2 systems | J-S chp 2 HO chp. 2 | 3 | |
| 6 | Hamiltonian systems Index theory | J-S chp 2 J-S: chp 3 | 4 | |
| 7 | Index theory Limit cycles and closed paths | J-S: chp 3 | 5 | |
| 8 | Poincare Maps Periodic solutions Poincare Bendixon's thm. | J-S: chp 13.1 J-S: chp 11 HO chp. 6 | 6 | |
| 9 | Periodic solutions Poincare Bendixon's thm. | J-S: chp 11 HO chp. 6 | 7 | |
| 10 | Stability Linear nxn equations | J-S: chp. 8 HO chp. 3 and 4 | 8 | |
| 11 | Stability Linear nxn equations | J-S: chp. 8 HO chp. 3 | 9 | |
| 12 | Linearization Hartman-Grobman theorem (self-study) Liapunov methods | J-S: chp. 10 HO chp. 3 | 10 | Read yourself: HO pp. 23-24 |
| 13 | Bifurcations Fractals and Iterated function systems | J-S: chp 12 HO note | 11 | |
| 14 | Fractals and Iterated function systems Discrete dynamical systems | HO note | 12 | |
| 15 | Discrete dynamical systems and chaos Summary and exam problems | HO note | 13 | |
| 16 | Easter | |||