Lecture plan/topics

This plan will be updated throughout the semester. P refers to the book by Perko, SC to the one by Schaeffer and Cain, and T to the one by Teschl.

Day	Topic	Sections	Repetition	Assumed knowledge from other courses
8.1	Introduction		Repetition
	Linear systems with a diagonalizable matrix	P: 1.1-1.2		Eigenvalues, Eigenvectors of a matrix, Diagonalization of a matrix
11.1	Linear systems with a diagonalizable matrix	P: 1.1-1.2	Repetition
	Linear systems: The fundamental solution	P: 1.3-1.4		Convergence of sequences and series in \(\mathbb{R}\)
15.1	Linear system: The fundamental solution	P: 1.3-1.4	Repetition
	Linear systems in \(\mathbb{R}^2\)	P: 1.5
18.1	Linear systems in \(\mathbb{R}^2\)	P: 1.5	Repetition
	Linear systems in \(\mathbb{R}^n \)	P: 1.6-1.8
22.1	Stability	P: 1.9	Repetition
25.1	Nonhomoegeneous systems	P: 1.10	Repetition	Differentiability and continuity
	Existence and uniqueness	P: 2.1-2.2, 2.4
29.1	Existence and uniqueness	P: 2.1-2.2, 2.4	Repetition
1.2	Existence and uniqueness	P: 2.1-2.2, 2.4	Repetition
	Dependence on parameters and initial data	P: 2.3 (Gronwall)
5.2	Dependence on parameters and initial data	P: 2.3 (Gronwall), Note	Repetition
	Flow	P: 2.5
8.2	Flow	P: 2.5	Repetition
	The stable manifold theorem	P: 2.6-2.7
12.2	The stable manifold theorem	P: 2.6-2.7	Repetition
	Hartman-Grobman theorem	P: 2.8, 2.10
15.2	Hartman-Grobman theorem	P: 2.8, 2.10, Note	Repetition
19.2	Hartman-Grobman theorem	P: 2.8, 2.10, Note	Repetition
	Sketching phase diagrams	SC: 4.4, 6.7
22.2	Liapunov functions	P: 2.9	Repetition	Graph of a function of several variables
26.2	Hamiltonian systems	P: 2.14	Repetition	Classifying extremal points of functions
29.2	Limit sets	P: 3.2	Repetition	Length of a curve
	Periodic solutions	SC: 7.1.1
4.3	Periodic solutions	SC: 7.1.1	Repetition
	Poincare Bendixson	P: 3.7
7.3	Poincare Bendixson	P: 3.7	Repetition
11.3	Lienard systems	P: 3.8	Repetition
14.3	Bendixson's criteria	P: 3.9	Repetition
	Index theory	P: 3.12
18.3	Index theory	P: 3.12	Repetition
21.3	Index theory	P: 3.12	Repetition
	Stability of limit cycles	P: 3.4, 3.5 or SC: 7.3		In the lecture we will follow SC.
4.4	Stability of limit cycles	P: 3.4, 3.5 or SC: 7.3	Repetition	In the lecture we will follow SC.
8.4	Stability of limit cycles	P: 3.4, 3.5 or SC: 7.3	Repetition	In the lecture we will follow SC.
11.4	Chaos	T: 10.1, 10.2 (def periodic orbit), 11.1-11.5	Repetition
15.4	Chaos	T: 10.1, 10.2 (def periodic orbit), 11.1-11.5	Repetition
18.4	Chaos	T: 10.1, 10.2 (def periodic orbit), 11.1-11.5	Repetition	11.5: Only the shift map \(\Sigma_2\).
22.4	???