University of Toronto at
Mississauga
Spring 2008
Course Outline
MAT 332H5S, Introduction to Nonlinear Dynamics and Chaos
- Instructor: Michael Yampolsky, Room 4061
- e-mail: yampol@math.utoronto.ca
- Lectures: Tuesdays 3pm-5pm, and Thursdays 3pm-4pm, Room SE 1143 Note the room change -- effective Thu, Jan 10!
- Office hours: Tuesdays 12-1pm, Thursdays 12-1pm or by appointment
- TA: Alex Shlakhter, shlakht@math.utoronto.ca
Tutorial sessions: Mondays 12-1pm, Room SE1154 Note the room change!, Office hours: Mondays 11am-12pm, Room SE 4061
- Textbook: An Introduction to Nonlinear Systems, Continuous
and Discrete, by Clark Robinson. 1st Edition, Pearson Education, 2004.
- 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.
- Web Page: http://www.math.utoronto.ca/~yampol/MAT332Spring2008.html
Marking scheme:
- 50% bi-weekly take home assignments.
- 15% Midterm, March 6, in class
- 35% 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.
Office hours before the exam: 10am-12pm Tuesday, April 15.
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 explaining why a saddle is called a "saddle"
- 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 an example of a gradient flow (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 predator-prey systems (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).
- Click here to see a Java simulation of the
iterated logistic map. This Java applet was kindly made available to the
Web community by A. Burbanks http://www.maths.bris.ac.uk/~maadb/