Lecture plan/topics

This plan will be updated throughout the semester. J.S. refers to the book by Jordan and Smith. H. refers to the note by Hanche-Olsen.

Day	Topic	Sections	Remarks
11.1	Intorduction	J.S: 1.1-1.3	Repetition
12.1	Introduction	J.S: 1.1-1.3	Repetition
	Well-posedness, uniqueness	H: Ch. 1
18.1	Well-posedness, uniqueness	H: Ch. 1	Repetition
19.1	Well-posedness, uniqueness	H: Ch. 1	Repetition
	Linear 2x2 systems	J.S: 2.4-2.6
25.1	Linear 2x2 systems	J.S: 2.4-2.6	Repetition
	Nonlinear 2x2 systems	J.S: 2.1, 2.8
26.1	Nonlinear 2x2 systems	J.S: 2.1, 2.8	Repetition
1.2	Nonlinear 2x2 systems	J.S: 2.3, 2.7	Repetition
		H: Ch. 2
2.2	Nonlinear 2x2 systems	J.S: 2.3, 2.7	Repetition
		H: Ch.2
8.2	Nonlinear 2x2 systems	J.S: 2.2	Repetition
	Stability	J.S: 8.1-8.4
9.2	Stability	J.S: 8.1-8.4	Repetition
	Linear systems	J.S: 8.5-8.6
15.2	Linear systems	J.S: 8.5-8.6	Repetition
	Stability	J.S: 8.7-8.8
16.2	Stability	J.S: 8.7-8.8	Repetition
	Matrix exponential	J.S: 8.8, 10.9
22.2	Matrix Exponential	J.S: 8.8 10.9	Repetition
	Stability	J.S: 8.9-8.11
23.2	Stability	J.S: 8.9-8.11	Repetition
	Liapunov methods	J.S: 10.1, 10.3
1.3	Liapunov methods	J.S: 10.3, 10.6-10.7	Repetition
2.3	Liapunov methods	J.S: 10.8, 10.10	Repetition
8.3	Liapunov methods	J.S: 10.10	Repetition
	Homoclinic / Heteroclinic phase paths	J.S: 3.6
9.3	Index theory	J.S: 3.1	Repetition
15.3	Index theory	J.S: 3.1	Repetition
	Limit cycles and closed paths	J.S: 3.4
16.3	Index theory	J.S: 3.2	Repetition
	Bifurcations	J.S: 12.1-12.4
22.3	Project	Traveling wave solutions for the Korteweg-de Vries equation	no lecture
23.3	Project	Traveling wave solutions for the Korteweg-de Vries equation	no lecture
5.4	Bifurcations	J.S: 12.1-12.4	Repetition
6.4	Poincare Bendixson	H: Ch. 6	Repetition
12.4	Poincare maps	J.S: 13.1	Repetition
	Periodic solutions	J.S: 11.1
13.4	Periodic solutions	J.S: 11.2-11.3	Repetition
19.4	Periodic solutions	J.S: 11.3 (There is a mistake in Thm 11.4)	Repetition
	??
20.4	??