Lectures for Math 634

Lectures
Lecture Number Title Date Given
1 ODEs and Dynamical Systems August 30
2 Existence of Solutions September 1
3 Uniqueness of Solutions September 3
4 Picard-Lindelöf Theorem September 8
5 Intervals of Existence September 10
6 Dependence on Parameters September 13
7 Constant Coefficient Linear Systems September 15
8 Understanding the Matrix Exponential September 17
9 Generalized Eigenspace Decomposition September 20
10 Operators on Generalized Eigenspaces September 22
11 Real Canonical Form September 24
12 Solving Linear Systems September 27
13 Qualitative Behavior of Linear Systems September 29
14 Exponential Decay October 1
15 Nonautonomous Linear Systems October 4
16 Nearly Autonomous Linear Systems October 6
17 Periodic Linear Systems October 8
18 Invariant Sets and Limit Sets October 11
19 Regular and Singular Points October 13
20 Definitions of Stability October 15
21 Principle of Linearized Stability October 18
22 Lyapunov's Direct Method October 20
23 LaSalle's Invariance Principle October 22
24 Hartman-Grobman Theorem, Part 1 October 25
25 Hartman-Grobman Theorem, Part 2 October 27
26 Hartman-Grobman Theorem, Part 3 October 29
27 Hartman-Grobman Theorem, Part 4 November 1
28 Hartman-Grobman Theorem, Part 5 November 3
29 Constructing Conjugacies November 5
30 Smooth Conjugacies November 8
31 Stable Manifold Theorem: Part 1 November 10
32 Stable Manifold Theorem: Part 2 November 12
33 Stable Manifold Theorem: Part 3 November 15
34 Stable Manifold Theorem: Part 4 November 17
35 Stable Manifold Theorem: Part 5 November 19
36 Stable Manifold Theorem: Part 6 November 22
37 Center Manifolds November 29
38 Computing and Using Center Manifolds December 1
39 Poincaré-Bendixson Theorem December 3
40 Lienard's Equation December 6
41 Lienard's Theorem December 7
Entire Semester (1.3 MB)
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