Jean-Luc Thiffeault's Homepage

Math 415 Applied Dynamical Systems, Chaos and Modeling: Fall 2017


Lecture Room: B239 Van Vleck
Lecture Time: 9:30–10:45 TR
Lecturer: Jean-Luc Thiffeault
Office: 503 Van Vleck
Email: jeanluc@[domainname],
where [domainname] is math point wisc point edu
Office Hours: Tuesdays 10:45–11:45; Thursdays 1:30–2:20

Final exam

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:

Syllabus

See the official syllabus.

Textbook

The textbook for the class is Nonlinear Dynamics and Chaos by Steven Strogatz (Second Edition).

Prerequisites

Math 319 or 320, or consent of instructor.

Homework

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

Piazza

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.

Schedule of Topics

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

Course Policy and Grading

There will be a midterm exam in class and a final exam. The final grade will be computed according to:

Homework35%
Midterm exam30%
Final exam35%

Exam Dates

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)

Midterm Results

# of scores 53
mean score 65.4
standard deviation 19.5
median score 64

Midterm solutions