AMATH 402
SLN 10208 (section A), SLN 10209 (section B, EDGE), SLN 19281 (section C)
MTWF 1:30-2:20, Loew Hall 216
http://www.amath.washington.edu/courses/402-winter-2008
(Prerequisites: AMATH 351, MATH 136, or MATH 307)

Introduction to Dynamical Systems and Chaos



Instructor:

Bernard Deconinck
Guggenheim 415J
tel: 543-6069
fax: 685-1440
bernard@amath.washington.edu
Office hours: M10:00-11:00am; T10:00-12:00pm

Teaching Assistant:

Mingyuan Zhong






Description Textbook syllabus objectives moodle grades

Course Description

Overview of methods to describe the qualitative behavior of solutions of nonlinear differential equations. Phase space analysis of fixed points and periodic orbits. Bifurcation methods. Description of strange attractors and chaos. Introductions to maps. Applications from engineering, physics, chemistry and biology.

Textbook

The required textbook for this course is Nonlinear Dynamics and Chaos, by Steven H. Strogatz, Perseus Books Group, 2001. This book provides a very readable introduction to dynamical systems, with lots of applications from a large variety of areas sprinkled throughout. This book is available from the University Bookstore. I did not find a better price anywhere else, after patronage refund.

Two other recommended books are (1) Dynamics: the geometry of behavior, by Ralph Abraham and Christopher Shaw, Aerial Press, 4th edition, 2005. This book contains a lot of pictures and some words. Going through this book allows one to build up a lot of intuition about dynamical systems. If it is true that a picture is worth a 1000 words, then this book is worth about a million words, with its 849 illustrations. Note that currently this book is only available as 4 pdf files on a CD. (2) Differential Equations, Dynamical Systems, and an Introduction to Chaos, by Morris W. Hirsch, Stephen Smale, and Robert Devaney, Academic Press, 2003. A classic texts by some of the true masters of the field, including some who helped shape it. This book is a bit more theoretical than the one we're using.
Lastly, during the course of the quarter, I will type up my lecture notes. They can be found on the moodle page, see below. Please save a few trees and don't print out the entire updated version on a weekly basis!

Syllabus

On MWF, we will follow Strogatz' book, covering at least the following topics:
(1) One-dimensional systems
Flows on the line
Bifurcations
Flows on the circle
(2) Two (and higher)-dimensional flows
Linear systems
The phase plane
Limit cycles
Bifurcations
(3) Chaos
The Lorenz equations
One-dimensional maps
Fractals
Strange attractors
On Tuesdays, we will expand on topics that the Strogatz book only touches on, or we will take time to talk about assignments, problems, etc.

Learning Objectives and Instructor Expectations

This is a class that will require you to work hard. Dynamical systems is a fascinating topic with lots of applications. The methods involved are not impossibly hard, but they cannot be mastered by spectators. Thus, participation in class and working out the homework problems are essential. We will also look at numerous applications, placing the material in a real-world context, from which it originated.

I will let you know clearly what you need to learn, what is important, and what is not. There will be plenty of homework. This is used to reinforce class lectures, not as a way to introduce new material. Exams will emphasize basic techniques as applied to simple, fundamental problems.

It is your responsibility to ask for help when you feel you need it. This is accomplished in class by asking questions and/or slowing me down, and outside of class by coming to office hours, for instance. Provided you are willing to work hard, it is my intention to provide you with as much help as you may need.

Watch video feeds of the lectures

Because this class is also offered through EDGE, the lectures are videotaped. You can view streaming video of the lecturers (including live performances!) here.

Moodle: homework, discussions, file downloads, etc

I'm trying something new for this course: we'll be using a moodle page for in-course communication, related to homeworks, scheduling, etc. You will find the lecture notes and the homework assignments there, as well as due dates, and solutions (cunningly posted after the due date!) Note that when you login, you will also see a moodle page for your specific section. Do not use it, as it may be outdated and incomplete. All relevant information is posted on the master page for Amath402, accessible by all sections.

Grading

Your course grade will be calculated by weighing your homework, midterm and final exam in the proportions 50%, 15% and 35%, respectively.

Homework sets are assigned weekly. Homework is due at the beginning of class on its due date. Late homework is not accepted, as homework solutions are posted immediately after class. Every homework set you hand in should have a header containing your name, student number, due date, course, and the homework number as a title. Your homework should be neat and readable. The TA is very much allowed to subtract points for presentation. Your lowest homework score will be dropped. This is meant as a way to deal with any emergencies which may occur (sickness, honeymoon, etc).

There will be an in-class midterm exam (50 minutes) for 15% of your grade, and an in-class final exam (110 minutes) for 35% of your grade. For either exam, you are allowed to use anything non-electronic.

If all things moodle work out, your scores and grades will be available on the moodle page, maybe after a few weeks.

<bernard@amath.washington.edu>