Lecture plan/topics
This plan will be updated throughout the semester. Sections refer to the book by Schaeffer and Cain.
Day | Topics | Sections | Remarks |
---|---|---|---|
1.9 | Introduction to ODEs | 1.1,1.2,1.3 | |
1.10 | Introduction to ODEs and linear systems | 1.4,1.5,1.6,2.2 | |
1.16 | The matrix exponential | 2.2 | |
1.17 | Existence and uniqueness for linear homogeneous systems | 2.2,2.3 | |
1.23 | Large-Time behaviour and Phase Portraits for linear systems | 2.4,2.5 | |
1.24 | Phase Portraits for linear systems; Nonlinear systems: Local theory | 2.5,3.1 | |
1.30 | The Contraction Mapping Theorem | 3.2 | |
1.31 | Existence theory for nonlinear systems; Gronwall Lemma | 3.2,3.3 | |
2.6 | The Uniqueness Theorem; Maximal solutions | 3.3,4.1 | |
2.7 | Global existence and trapping regions | 4.2.1,4.2.2 | |
2.13 | Trapping regions, Nullclines and Applications | 4.2.2, 4.4 | |
2.14 | Continuity properties of the solution; the Flow Map | 4.5 | |
2.20 | Continuity with respect to parameters; differentiability of the Flow Map | 4.5.3, 4.6.1, 4.6.2, 4.6.5, 4.6.6 | |
2.21 | Trajectories near Equilibria | 6.1.1, 6.2.1 | |
2.27 | Trajectories near Equilibria, Lyapunov Functions | 6.2.2, 6.2.3, 6.2.4, 6.5.1 | |
2.28 | Lyapunov Functions, Lasalle's Invariance Principle | 6.5.1, 6.5.2, 6.5.3 |
SC refers to the book by Schaeffer and Cain.
Day | Topic | Sections |
---|---|---|
6.3 | Stable and unstable manifolds | SC: 6.6.1-6.6.2 |
7.3 | Stable and unstable manifolds | SC: 6.7, 6.9.2 |
13.3 | Index theory | SC: 7.11* |
14.3 | Index theory | SC: 7.11* |
20.3 | Index theory | SC: 7.11* |
Periodic solutions | SC: 7.1-7.2 | |
21.3 | Periodic solutions | SC: 7.1-7.2 |
27.3 | Periodic solutions | SC: 7.1-7.2 |
Stability of periodic solutions | SC: 7.3 | |
28.3 | Stability of periodic solutions | SC: 7.3 |
17.4 | Stability of periodic solutions | SC: 7.3 |
18.4 | Stability of periodic solutions | SC: 7.3 |
24.4 | Bifurcation | SC: 8.1, 8.3, 8.4,8.5 (only p. 341-342), 8.7 |
25.4 | ??? |
* This chapter cannot be found in the version downloaded from Springer. See the general infomation page → books and reading material for a link.