Final Exam
presentation: Friday, May 5th from 8:00 - 10:00 in S 155.
Textbook:
Nonlinear
Dynamics and Chaos with Applications to Physics, Biology, Chemistry and
Engineering by Steven H. Strogatz Class
43 Mon May 1: Properties
of the Lorenz Equations; chaos. Class
42 Fri April 28: Read Sections 9.0, 9.1, & 9.2:
Properties of the Lorenz Equations. Class
42 Wed April 26: Read Sec 7.3: Poincare-Bendixson
Theorem. Practice 7.1.5 on p.228; 7.3.8 on p.232. Class
41 Mon April 24: Read about limit cycles, the van
der Pol oscillator, Liapunov functions: Section 7.0, 7.1, & 7.2. Practice
7.2.10 on p. 230. Class
40 Wed April 19: Asmir
Taletovic: Reversible Systems in Section
6.6. Today,
turn in 6.3.2 on p. 182; the phase portrait may be done with Maple. Class
39 Mon April 17: Mark
Wilkinson: Conservative
Systems in Section 6.5. Class
38 Fri April 14: Brian
Volante:
"Love Affairs" (linear systems) Katie
Baxter: "Rabbits
versus Sheep" (Lotka-Volterra model of competition). Class
37 Wed April 12: Read 6.3: Hyperbolic fixed
points; Hartman-Grobman theorem. On Monday, turn in 6.3.2 on p. 182;
the phase portrait may be done with Maple. Class
36 Mon April 10: Read 6.3: Fixed Points and
Linearization. Class
35 Fri April 7: Phase Portraits of Nonlinear Systems:
read Sections 6.0, 6.1, & 6.2. Bonus:
For Problem 6.1.6 on p.181, find the equation of the stable manifold of
the saddle point. Class
34 Wed April 5: The "Determinant-Trace Test" for determining
the phase portraits of linear homogeneous systems. On
p.143, turn in 5.2.6, 5.2.8, & the LRC circuit problem: 5.2.12
(in part (c) select values to illustrate the three cases and use Maple
to draw the phase portraits. Class
33 Mon April 3: Turn in 5.2.2 p.142; also use Maple to
draw the phase portrait. Class
32 Fri March 31: Turn in on Monday p.141 : 5.1.9; also
prove the formulas relating det A & Tr(A) with the eigenvalues of A
on the 3rd line of p.137. Class
31 Wed March 29: Turn in on Friday p.140 : 5.1.1 and 5.1.2. Class
30 Mon March 27: Experiment with the Maple worksheet "Phase
Portraits of Planar Linear Systems." Read
Section 5.2. Practice p.141 : 5.1.2. Class
29 Fri March 24: Experiment with the Maple worksheet "Simple
Harmonic Motion." Turn in p.140: 5.1.4, 5.1.5, 5.1.7. Class
28 Wed March 22: Read Sec 5.0 & 5.1. Overdamped
pendulum driven by a constant torque by Chris
Vick. Class
27 Mon March 20: Synchrony of flashing of male fireflies
by Lewis Pearson. Class
26 Fri March 17: Ghosts and bottlenecks in nonuniform oscillators.
For Monday, read about the overdamped pendulum driven by a constant torque
in Section 4.4. Also, read about the synchrony of flashing
of male fireflies in Sec 4.5 in preparation for the talk by Lewis Pearson.
Lewis's talk will be followed by one given by Chris Vick. Class
25 Wed March 15: Read Section 4.3. TI p.113: 4.2.3
(the clock problem). Class
24 Mon March 13: Turn in p. 85: 3.5.5 (not 3.5.6 unless
you have already done it) and 3.5.7. Read
Sections 4.0, 4.1, 4.2. PR p.113: 4.1.3, 4.2.1, and 4.2.3. Class
23 Fri March 3: Phase plane analysis of the overdamped bead on
a rotating hoop / Maple demonstration. On Wed March 15, turn in p.
85: 3.5.6 ( one physical analog is sufficient) and 3.5.7. Class
22 Thurs March 2: (Make-up class)
Special lecture by Bill Mason.
Subcritical Pitchfork Bifurcation / Stabilizing influence of higher-order
terms / hysteresis. Class
21 Wed March 1: Dimensional analysis and scaling. ( Remember
make-up class tomorrow at 1:00.) Class
20 Mon Feb 28: Analysis of the first-order system modeling the
angular displacement of the overdamped bead on a rotating hoop. Turn
in p. 84: 3.5.2. Class
19 Fri Feb 25: Read Sec 3.5: Overdamped bead on a rotating
hoop. Turn in p.82: 3.4.2 (analyze graphically breaking up into two
parts: x' = rx & x' = sinh x. (References: the way
I worked Example 3.4.1 & the solution of Problem 3.2.4). Also,
p.84: 3.4.16 part (a). Class
18 Wed Feb 23: Example 3.4.1 - analysis of a differential
equation that arises in models of magnets & neural networks. Class
17 Mon Feb 21: Read Sec 3.4. PR p. 82: 3.4.2 Class
16 Fri Feb 18: Special lecture by Roberto
Martinez on how lasers operate and an improved
model of the laser threshold. Turn
in 3.3.1 (a), (b), (c) about an improved model of the laser. Read
Sec 3.4. Class
15 Wed Feb 16: Practice p.80: 3.2.2.
Turn in p.80: 3.2.4. Read Sec 3.3. Class
14 Mon Feb 14: Turn in p.79: 3.1.2.
Read Sec 3.2. Class
13 Fri Feb 11: Practice p.79: 3.1.1 &
3.1.2. Read Sec 3.2 about transcritical bifurcations. Class
12 Wed Feb 9: No class. On Friday, turn in
p.41: 2.5.6. PR p.42: 2.7.1 & 2.7.5. Read Sec
3.0 & 3.1. Class
11 Mon Feb 7: No class. Class
10 Fri Feb 4: Turn in p.41: 2.5.6.
PR p.42: 2.7.1 & 2.7.5. Read Sec 3.0 & 3.1. Class
9 Wed Feb 2: Read Sec 2.6 & 2.7.
Turn in p.41: 2.5.6 on Monday. Class
8 Mon Jan 31: Turn in on Friday: p.39: 2 .3.2,
2.4.4, 2.4.9. Practice p. 40: 2.5.1 & 2.5.4. Class
7 Fri Jan 28: All CBU classes cancelled due to snow. Class
6 Wed Jan 26: Read pp. 24-28. Practice
p. 38: 2.3.1, 2.3.2, 2.4.5, 2.4.6 . Class
5 Mon Jan 24: Turn in p. 36: 2.2.3 & 2.2.11.
Practice p. 37: 2.2.7. Class
4 Fri Jan 21: Turn in p. 36: 2.1.2, 2.1.4.
Practice p. 36: 2.1.1, 2.1.3, 2.2.1. Class
3 Wed Jan 19: Read pp. 15 - 24. Class
2 Fri Jan 14: TI Problems 1 & 2 on Homework
Sheet. Class
1 Wed Jan 12: Read Chapter 1 Overview pp. 1-11. Experiment
with the Maple worksheet "Butterfly".