University of Toronto at Mississauga
Fall 2018

Course Outline
MAT 332H5S, Introduction to Nonlinear Dynamics and Chaos

Instructor: Michael Yampolsky, Room DH-3022
e-mail: yampol(at)math(dot)utoronto(dot)ca
Lectures: Tue, 03:00 PM - 05:00 PM DV 1160
Thu, 01:00 PM - 02:00 PM DV 1160
Office hours: Tue/Thu 11-12
Office hours before the final exam: Thursday December 6, 11-12:30
TA: Yulia Bibilo, yulia(dot)bibilo(at)utoronto(dot)ca
TA's office hours: Monday 12-1, DH3064
Textbook: An Introduction to Dynamical Systems, Continuous and Discrete, by Clark Robinson. 2nd Edition, American Mathematical Society.
Other suggested reading. The following books are not required for the course. You may, however, find them interesting and useful: Devaney, "A first course in chaotic dynamical systems", and "Introduction to chaotic dynamical systems"; Lynch "Dynamical systems with applications using MAPLE"; Strogatz "Nonlinear dynamics and chaos. With applications to physics, biology, chemistry, and engineering".
Computing projects: The computational side of the course will be based on the use of a powerful computer algebra system Maple. Please click here for the links to Maple resources. The author of the textbook also has some sample Maple worksheets on his web page.
Using Maple at UTM: go to http://xenweb.utm.utoronto.ca/. If this is the first time you are using it, you will need to install Citrix receiver on your computer. After that, use your UTORId to log in, and you will have Maple as one of the available apps on your screen.
Web Page: http://www.math.utoronto.ca/yampol/MAT332Fall2018.html

Marking scheme:

40% bi-weekly take home assignments.
20% Midterm, October 25, in class
40% Final Exam

IMPORTANT: Please note that there will be no make-up tests, an undocumented absence will result in zero credit. No late assignments will be accepted. A late hand-in will also result in zero credit.

Click here for the first assignment. Due on Thursday, September 27, in class.

Click here for the second assignment. Due on Thursday, October 18, in class.
Click here for the third assignment. Due on Thursday, November 8, in class.
Click here for the fourth assignment. Due on Thursday, November 29, in class.

Click here for the suggested homework exercises.

Supporting materials.

Click here for the supporting materials for Chapter 1: numerical study of linear and nonlinear oscillators; examples of chaos: double pendulum, forced simple pendulum.
Right-click here to save a Maple worksheet with examples of linear systems with constant coefficients for Chapter 2.
Right-click here to save a Maple worksheet with examples of linear systems with quasi-periodic solutions (Chapter 2). Here is a Java simulation of a double spring from myphysicslab.com.
Right-click here to save a Maple worksheet with examples of limit sets (Chapter 4).
Right-click here to save a Maple worksheet with examples of phase portrait study of nonlinear systems in 2D (Chapter 4).
Right-click here to save a Maple worksheet with examples of phase portrait study of nonlinear systems using energy-type functions (Chapter 5).
Right-click here to save a worksheet with a study of periodic orbits (Chapter 6).
Right-click here to save a worksheet with examples of oscillating chemical reactions (Chapter 6)
Right-click here to save a worksheet with an example of a Lienard system (Chapter 6).
Right-click here to save a worksheet with examples of bifurcations in 2D phase portraits (Chapter 6).
Right-click here to save a worksheet with examples of a Poincare map in a 2D system (Chapter 6).
Right-click here to save a worksheet with a study of chaos in the Lorenz system (Chapter 7).
Another example of chaos -- forced nonlinear oscillator. The worksheet includes the study of the Poincare map (Chapter 7).
Right-click here to save a worksheet with examples of graphical iteration (Chapters 8 and 9).

Plagiarism and academic honesty: Students are expected to adhere to the academic regulations of the University as outlined in the "Code of Behaviour on Academic Matters" which can be found in the UTM Calendar.

The work you submit must be your own. Plagiarism is a form of academic fraud, and the University treats it very seriously. See the guide How Not to Plagiarize.

IMPORTANT NOTE on PRE- and CO-REQUISITES: pre/co-requisites will be checked, and students without them will be removed from the course before September 19, 2018 (they will receive an e-mail informing them of their removal from a course). If a student believes that s/he does have the necessary background material, and is able to prove it (e.g., has a transfer credit from a different university), then s/he should submit a 'Prerequisite/Corequisite Waiver Request Form', which can be found by clicking here. The student should complete Part A of the form and submit it to the instructor, by September 12, 2018. Students must give a reason for requesting a waiver. Simply submitting the form does not mean they can stay in the course.