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.

DayTopicSections
6.3Stable and unstable manifolds SC: 6.6.1-6.6.2
7.3Stable and unstable manifolds SC: 6.7, 6.9.2
13.3Index theorySC: 7.11*
14.3Index theorySC: 7.11* 
20.3Index theorySC: 7.11* 
Periodic solutionsSC: 7.1-7.2
21.3Periodic solutionsSC: 7.1-7.2
27.3Periodic solutions SC: 7.1-7.2
Stability of periodic solutionsSC: 7.3
28.3Stability of periodic solutionsSC: 7.3 
17.4Stability of periodic solutionsSC: 7.3 
18.4Stability of periodic solutionsSC: 7.3
24.4Bifurcation 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.

2024-07-05, Katrin Grunert