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

PicardLindelöf 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

HartmanGrobman Theorem, Part 1

October 25

25

HartmanGrobman Theorem, Part 2

October 27

26

HartmanGrobman Theorem, Part 3

October 29

27

HartmanGrobman Theorem, Part 4

November 1

28

HartmanGrobman 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

PoincaréBendixson Theorem

December 3

40

Lienard's Equation

December 6

41

Lienard's Theorem

December 7
