MAT 267H1: Advanced Ordinary Differential Equations
Winter 2019

Professor: Mary Pugh
Contact information: mpugh@math. utoronto.ca
Office hours: Mondays 11-12 and 1-2 in PG 003, Wednesdays 1-2 in BA6268
Office location: Bahen 6268

Meeting time and place: The class meets on Tuesdays 1:10-2pm and Thursdays 1:10pm-3pm in WB116. The first lecture will be on on Tuesday January 8 and the last on Thursday April 4. There are two tutorial sections; students need to enrol in one and attend that tutorial. Tutorials meet Friday 1:10-2 and 3:10-4, starting on January 18.

Syllabus

Errors in "Differential Equations, Dynamical Systems, and an Introduction to Chaos" by Hirsch, Smale, and Devaney.

Schedule, Suggested Readings, exercises, lecture notes, quiz solutions, etc

Request for Volunteer Note Taker:
Accessibility Services is asking for a volunteer note taker for this course. All you have to do is attend classes regularly & submit them consistently.
Step 1: Register Online as a Volunteer Note-Taker at this site .
Step 2: Select your course and click Register
Step 3: Upload your notes after every class
Email as.notetaking@utoronto.ca or call 416-978-6186 if you have questions. Volunteers may receive co-curricular credit or a certificate of appreciation.

Extra resources:
Eckhard Meinrenken's 2018 MAT267H1 website.
Dmitry Panchenko's 2017 MAT267H1 website. You can find his lecture notes there. Here's a proof of Peano's Existence Theorem that doesn't rely on the Arzela-Ascoli theorem (as does the argument in Dmitry's notes).
Online notes by Paul Dawkins.

Computer stuff:
I will occasionally use matlab in class and will provide primitive matlab code for you to study and modify, should you wish. You have free access to matlab, as a UofT undergrad. Just go here. Also, there are various free matlab clones that you can install on your computer if you wish.
Crash courses on matlab Here's Cleve Moler's "Introduction to MATLAB" chapter from his textbook.
How about some python? An open-source software that's well worth looking into is SciPy. It's a python-based scientific computing environment. Our physics department has a lovely python wiki which includes lessons on how to use python as well as an easy-to-install python package.

On-line demos:
Direction field plotter from Geogebra
Another direction field plotter, by Darryl Nester. When using his plotter for tricky direction fields, you might want to play around with the four possible time-steppers (Euler, Heun, Midpoint, Fourth-order Runge-Kutta, and Runge-Kutta 3/8 Method) as well as exploring the effect of using switching.
Understanding and plotting vector fields can be tricky because you care about the magnitudes of the vectors but the vectors can get in the way of one another. Here's a vector field plotter which uses particle trajectories as a way of helping visualize vector fields. Try hitting "Randomize" a few times!