University
of Toronto at Mississauga
Fall 2015
Office hours before the final exam: Monday, Dec 14, 11am-1pm
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: Tuesdays 3pm-4pm, DV 3131 and Thursdays 2pm-4pm, IB 370
- Office
hours: Tuesdays 2-3, Thursdays 12-1 or by appointment
- TA: Miodrag Sokic
- e-mail: miodrag(dot)sokic(at)utoronto(dot)ca
- TA’s
office hours: Monday 12-2pm in DH2034
Practicals: Mondays 2-3pm, Room
DV 1092A
- 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.
- Web
Page: http://www.math.utoronto.ca/~yampol/MAT332Fall2015.html
Marking scheme:
- 40% bi-weekly take home assignments.
- 20% Midterm, October 20, 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 fourth assignment. Due on November 19th, 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 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 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.