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

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.

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.

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; 6.1–6.3 Two-dimensional linear flows (finish); Phase plane

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 TBA)