Course Outline

Date

Lct.

Sections

Topic

Assign.

9/6

1

Chap. 1

Introduction, Overview, Review

Sel. Probs.

9/10

2

Chap. 1, 2.0-2.2

 Overview, Review, Stability

Sel. Probs.

9/13

3

2.3 – 2.8

Population Dynamics, Potentials and Numerics

Sel. Probs.

9/17

4

3.0 – 3.3

Saddle-Node, Transcritical &  Pitchfork Bifurcations

Sel. Probs.

9/20

5

3.4, 3.5, Chap. 4

Imperfect Bifurcations, Flow on a Circle

Sel. Probs.

9/27

6

5.0 – 5.2

2D Linear Systems

Sel. Probs.

10/1

7

5.0 – 5.2, 6.0 – 6.2

2D Linear Systems, Phase Portraits

Sel. Probs.

10/4

8

6.3 – 6.5 + Notes

Fixed Points, Simulations and Lotka-Volterra Eqs.

Sel. Probs.

10/8

9

6.4

Conservative and Hamiltonian Systems

Sel. Probs.

10/11

10

6.4 + Notes

Conservative and Hamiltonian Systems

Sel. Probs.

10/15

11

 6.5

Conservative and Hamiltonian Systems

Sel. Probs.

10/18

12

6.7, 7.0 + Notes

Structural Stability, Peixoto’s Theorem

Sel. Probs.

10/22

13

7.1 – 7.3

Pendulum, Limit Cycles <Review for Midterm Exam>

Sel. Probs.

10/25

14

------------

Midterm EXAM

-----.

10/29

15

8.0 – 8.2

2D Bifurcations <BIG PROJECT ASSIGN (due 12/6)>

Sel. Probs.

11/1

16

8.3 – 8.4

Hopf Bifurcation

Sel. Probs.

11/5

17

8.6

Coupled Oscillators, Quasiperiodicity

Sel. Probs.

11/8

18

8.7 + Notes

 Poincaré Maps 

Sel. Probs.

11/12

19

9.0 – 9.4

Lorenz and related Equations 

Sel. Probs.

11/15

20

 10.0 – 10.2

Lorenz and related Equations 

Sel. Probs.

11/19

21

10.3 – 10.4

Logistic Map, Lyapunov Exponents

Sel. Probs.

11/20

22

10.5 – 10.6

Universality, Sharkovski’s Theorem

Sel. Probs.

11/22

---

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THANKSGIVING  BREAK

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11/26

23

11.0 – 11.2

Fractals and Fractal Dimensions

Sel. Probs.

11/29

24

11.3 – 11.4

Fractals and Fractal Dimensions

Sel. Probs.

12/3

25

12.0 - 12.3

Strange Attractors

Sel. Probs.

12/6

26

12.3 - 12.5

Henon and related Maps  <BIG PROJECT DUE>

Sel. Probs.

12/10

27

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Review for Final Exam