MAT 267H1: Advanced Ordinary Differential Equations
Winter 2020

Winter 2020

Professor: Mary Pugh
Contact information: mpugh@math. utoronto.ca
Drop-in hours: Tuesdays 2:10-3, Wednesdays 1:10-2 in BA 6268.
Also, I have drop-in hours for MAT187 Wednesdays 2:10-4 in PG 003. But MAT187 students will have higher priority during that time.

Meeting time and place: The class meets on Tuesdays 1:10-2pm in LM161 and on Thursdays 1:10pm-3pm in MP 102. The first lecture will be on on Tuesday January 7 and the last on Thursday April 2. There are two tutorial sections; students need to enrol in one and attend that tutorial. Tutorials meet Friday 1:10-2 in SS1070 and 3:10-4 in SS1072, starting on January 10.

Syllabus

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

Schedule, Suggested Readings, homework assignments/solutions, (occasional) lecture notes, etc

I'm only interested in pure math. Why should I care about this course? You simply can't do geometry or topology (at any serious level) without differential equations. In fact, they show up in all sorts of places. Here's a link that I found by googling "differential equations in pure math". Googling "differential equations used in number theory" led here. Googling "differential equations used in galois theory" leads to Differential Galois Theory which is then related to D-modules. And so forth and so forth. It even shows up in logic/theoretical computer science (google "computability and ODEs").

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. If you're already taking notes for yourself, why not share? You could make a real difference for a classmate!
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:
My 2019 MAT267H1 website.
Eckhard Meinrenken's 2018 MAT267H1 website.
Online notes by Paul Dawkins.

On-line demos:
Desmos is a webpage that will allow you to create simple plots, slightly less simple plots, interactive plots, and animations. You can get a shareable URL by clicking on the icon at the top right of the page that's a box with an arrow in it. Clicking there will also allow you to export the plot as a file to use as you wish.
Here's a nice parametric curve plotter by Christopher Chudzicki that can help you visualize solutions in R^3. There are also demos for parametric curves in R^2 and parametric surfaces in R^3.
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!

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.