Lecture Room: | B239 Van Vleck |
Lecture Time: | 9:30–10:45 TR |
Lecturer: | Jean-Luc Thiffeault |
Office: | 503 Van Vleck |
Email: | |
Office Hours: | Tuesdays 10:45–11:45; Thursdays 1:30–2:20 |
The final exam is on Thursday December 21 at 2:45pm, in the
regular classroom (B239). It will last 2 hours. The exam consists
of 4 questions. You are responsible for all the material in the
class, except as noted below, but the exam will lean heavily on the
post-midterm parts.
Here is a not-completely-exhaustive list of what you're expected to know:
See the official syllabus.
The textbook for the class is Nonlinear Dynamics and Chaos by Steven Strogatz (Second Edition).
Math 319 or 320, or consent of instructor.
Every two weeks or so I will assign homework from the textbook and post it here.
HW 1 (Due Sept 21 26): 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 10 12): page 80: 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 26): page 115: 4.1: 1–3; 4.3: 2, 3; 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 9 Nov 14): 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.
[6.3.2, 6.3.5: OK in this case to assume centers persist.]
Solutions
HW 5 (Due Nov 28): page 187: 6.5: 1, 2, 3, 11, 19; 6.7: 2 [except the 'reversible' question in (c)]; 6.8: 1, 3, 4, 5, 6, 8; page 230: 7.1: 1, 4, 8; 7.2: 2, 6, 10, 14; 7.3: 1, 3, 4. Solutions
We'll use Piazza Q&A for discussions about the class and related topics. Feel free to post questions and answers there about homeworks and exams, logistics, or relevant interesting things you found on the web. Note that we will only use Piazza for the Q&A feature, not for posting the actual homeworks.
lecture | date | sections | topic |
1 | 09/07 | 1 | Introduction |
2 | 09/12 | 2.1–2.4 | One-dimensional ODEs |
3 | 09/15 | 2.5–2.8 | Existence and uniqueness |
4 | 09/19 | 3.1 | Saddle-node bifurcations |
5 | 09/21 | 3.2–3.4 | Transcritical and pitchfork bifurcations |
6 | 09/26 | 3.5 | Overdamped bead |
7 | 09/28 | 3.6 | Imperfect bifurcations; catastrophes |
8 | 10/03 | 3.7 | Insect outbreak |
9 | 10/05 | 4 | Flows on the circle |
10 | 10/10 | 4.5; 5.1 | Fireflies; Two-dimensional linear flows |
11 | 10/15 | 5.2 | Two-dimensional linear flows (cont'd) |
12 | 10/17 | 5.2; 6.1 | Two-dimensional linear flows (finish); Phase plane |
13 | 10/19 | 6.1–6.3 | Phase plane (cont'd) |
14 | 10/24 | 6.4 | Lotka–Volterra model |
15 | 10/26 | – | Modeling plants in lake Wingra (notes) |
– | 10/31 | – | Homework Q&A |
– | 11/02 | – | MIDTERM (first three homeworks) |
16 | 11/07 | 6.5 | Convervative systems |
17 | 11/09 | 6.7, 6.8 | Pendulum; Index theory |
18 | 11/14 | 6.8, 7.1 | Index theory (cont'd); Limit cycles |
19 | 11/16 | 7.1–7.2 | Limit cycles (cont'd) |
20 | 11/21 | 7.3 | Poincaré–Bendixson Theorem |
21 | 11/28 | 9.2 | The Lorenz equations (Lorenz's paper) |
22 | 11/30 | 9.2–9.3 | The Lorenz equations: numerical demonstration (Matlab files) |
23 | 12/05 | 10.0–10.1 | One-dimensional maps |
24 | 12/07 | 10.2–10.4 | Periodic orbits of maps; Chaos (Matlab files) |
– | 12/12 | – | Discussion of final |
There will be a midterm exam in class and a final exam. The final grade will be computed according to:
Homework | 35% |
Midterm exam | 30% |
Final exam | 35% |
Midterm exam | Thursday November 2, 2017 at 9:30–10:45 | (in class) |
Final exam | Thursday December 21, 2017 at 14:45–16:45 | (room B239) |
# of scores | 53 |
mean score | 65.4 |
standard deviation | 19.5 |
median score | 64 |