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| Lecture Room: | 6203 Social Sciences Building |
| Lecture Time: | 11:00–12:15 TR |
| Lecturer: | Jean-Luc Thiffeault |
| Office: | 503 Van Vleck |
| Phone: | (608)263-4089 |
| Email: |
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| Office Hours: | 13:00-14:00 TR, or by appointment. |
See the official syllabus.
The textbook for the class is Nonlinear Dynamics and Chaos by Steven Strogatz.
Math 319 or 320, or consent of instructor.
Each two weeks I will assign homework from the textbook and post it here.
HW 1 (Due Sept 25): page 36: 2.1: 1–4; 2.2: 1–4, 7, 10, 13; 2.3: 1, 4; 2.4: 1, 3, 6, 9; 2.5: 1, 2, 4, 6; 2.7: 1, 3. Solutions
HW 2 (Due Oct 9): page 79: 3.1: 1–2; 3.2: 1, 2, 4; 3.3: 1 [except (d)]; 3.4: 1, 2, 4, 5, 7, 10, 11, 15; 3.5: 2, 3, 6 [except (e)]; 3.6: 2, 4; 3.7: 1–4. Solutions
HW 3 (Due Oct 23): page 113: 4.1: 1–3; 4.3: 2, 3, 4, 7; 4.4: 4; 4.5: 1, 3; page 140: 5.1: 3–6, 9, 10; 5.2: 1–4, 7, 10, 11, 13. Solutions
HW 4 (Due Nov 6): page 181: 6.1: 1, 2, 4, 6; 6.2: 2; 6.3: 1, 2, 4, 5, 9 (except (e)), 11, 13; 6.4: 3, 4. Solutions
HW 5 (Due Nov 20): page 185: 6.5: 1, 2, 3, 11, 19; 6.7: 2 [except the 'reversible' question in (c)]; page 228: 7.1: 1, 4, 8; 7.2: 2, 6, 10, 14; 7.3: 1, 3. 4. Solutions
HW 6 (Due Dec 11): page 342: 9.2: 1, 2 [except 'stiffer challenge']; page 388: 10.1: 10, 11; 10.3: 1, 4, 5, 7. Solutions [Correction: 10.1.11 x=0 should be unstable.]
| lecture | date | sections | topic |
| 1 | 09/02 | 1 | Introduction |
| 2 | 09/04 | 2.1–2.4 | One-dimensional ODEs |
| 3 | 09/09 | 2.5–2.8 | Existence and uniqueness |
| 4 | 09/11 | 3.1–3.2 | Bifurcations |
| 5 | 09/16 | 3.3–3.4 | Laser; pitchfork bifurcation |
| 6 | 09/18 | 3.5 | Overdamped bead |
| 7 | 09/23 | 3.6 | Imperfect bifurcations; catastrophes |
| 8 | 09/25 | 3.7 | Insect outbreak |
| 9 | 9/30 | 4 | Flows on the circle |
| 10 | 10/02 | 5.1 | Circle (cont'd); Two-dimensional linear flows |
| 11 | 10/07 | 5.1–5.3 | Two-dimensional linear flows (cont'd) |
| 12 | 10/09 | 5.1–5.3 | Two-dimensional linear flows (cont'd) |
| 13 | 10/14 | – | MIDTERM (first two homeworks) |
| 14 | 10/16 | 6.1–6.3 | Phase plane |
| 15 | 10/21 | 6.1–6.3 | Phase plane (cont'd) |
| 16 | 10/23 | 6.4–6.5 | Lotka–Volterra model; Convervative systems |
| 17 | 10/28 | 6.5, 6.7 | Conservative systems (cont'd); Pendulum |
| 18 | 10/30 | 7.1–7.2 | Limit cycles |
| 19 | 11/4 | 7.3 | Poincaré–Bendixson Theorem |
| 20 | 11/6 | 9 | The Lorenz equations and chaos |
| 21 | 11/11 | 9 | The Lorenz equations: numerical demonstration (Matlab files) |
| 22 | 11/13 | 9 | Chaos and strange attractors |
| 23 | 11/18 | 10.0–10.1 | One-dimensional maps |
| 24 | 11/20 | 10.2–10.3 | Period-doubling route to chaos; numerical demonstration of logistic map (Matlab files) |
| 25 | 11/25 | – | Guest lecture (numerical solution of ODEs) by Prof. Rossmanith |
| 26 | 12/02 | 10.3–10.4 | Periodic windows; Intermittency; Period-doubling |
| 27 | 12/04 | 10.5–10.6 | Lyapunov exponents for maps; Tent map; Universality |
| 28 | 12/09 | 10.6 | Universality (cont'd) |
| 29 | 12/11 | 11 | Period doubling in reality; Fractals |
There will be a midterm exam in class and a final exam. The final grade will be computed according to:
| Homework | 25% |
| Midterm exam | 25% |
| Final exam | 50% |
You can see where you midterm grade falls with respect to your peers (grades listed in decreasing order):
| out of 60 | % |
| 51 | 85.0 |
| 51 | 85.0 |
| 47 | 78.3 |
| 47 | 78.3 |
| 44 | 73.3 |
| 43 | 71.7 |
| 43 | 71.7 |
| 39 | 65.0 |
| 33 | 55.0 |
| 20 | 33.3 |
| 13 | 21.7 |
| 12 | 20.0 |
Here are the solutions to the midterm.
The midterm exam will be given during the regular 75 minute lecture period.
| Midterm exam | Tuesday October 14, 2008 at 11:00–12:15. |
| Final exam | Thursday December 18, 2008 at 12:25–14:25 (6203 Social Sciences Building) |
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Last modified: 14:05 16 December 2008 |
Background: Coarsening of a binary fluid (Simulations by Lennon Ó Náraigh) |