MAT 267 Ordinary Differential Equations, Winter 2021

Almut Burchard, Instructor

How to reach me:

Almut Burchard, BA 6234, 978-3318.

almut @math, www.math.utoronto.ca/almut/

Lectures: Tue 1:10-2pm, Thu 1:10-3pm; online

Office hours Tue 2:10-3pm

Tutorials Fri 10:10-11am (Almut), 1:10-2pm (Kosenko), or 3:10-4pm (Deaibes)

Schedule

Zoom link for lectures:   available on Qercus. If you are not registered for the course, I can send it to you by email.
Piazza (Use this as a forum. I will log in twice a week to participate and comment.)
If you need to speak to me privately, please send email or use my office hours

Teaching assistants:   Petr Kosenko, petr.kosenko@mail.utoronto.ca and Salim Deaibes, salim.deaibes@mail.utoronto.ca

Textbook:  "Differential Equations, Dynamical Systems, and an Introduction to Chaos" (3rd edition), by Morris W. Hirsch, Stephen Smale, and Robert L. Devaney.
library access

Course content:   Introduction to ordinary differential equations, for math specialists. The textbook is a more introductory version of the Hirsch & Smale classic "Differential Equations, Dynamical Systems, and Linear Algebra". We will cover Chapters 1-10 and 17. These provide the viewpoint needed to enter into the arena of nonlinear dynamics and dynamical systems. However, they do not contain some of the analytical material required for subsequent courses in geometry, analysis, and PDE; this will be provided when needed. We will also consider a few applications from Chapters 11-16.

1. What is an ODE? What do we mean by "solution"?
2. Techniques for obtaining explicit solutions: Separation of Variables, Variation of Constants, Undetermined Coefficients, exact equations
3. Initial-value problems. Existence, uniqueness, and continuous dependence. Picard iteration and Contraction Mapping Theorem
4. Planar systems. Phase portraits, classification
5. Linear systems in higher dimensions. The role of eigenvalues and eigenvectors
6. Equilibria in nonlinear systems. Linearization and stability
7. Vector fields and groups of diffeomorphisms
8. Global nonlinear techniques. Gradient systems, Hamiltonian systems
9. Closed orbits and limit sets
10. Applications in Geometry, Physics, and Biology

Evaluation:

• Homework.  +/- 10 problems per week. Please discuss freely, and use any source you find useful!
• Quizzes.   Once-a-week short quizzes based on one homework problem (2:50pm Thursdays / 2:50am Fridays). Quizzes are marked 0, 1, 2 (drop one).
• Hand-in Problem Sets. More substantial problerms, with detailed instructions. Due on Jan 30, Feb 13, March 6, March 20, and April 3 (all Saturdays, at midnight).
• Midterm Assessments.   February 8, March 15 (both Mondays)
• Final Assessment.  TBD (between April 13 and 23). Counts for 2 parts.

Marking Scheme: The course mark has six (6) equal parts: Quizzes, Problem Sets, Midterm 1, Midterm 2, Final, Final (counted again).
Of these the lowest mark is dropped and the remaining five (5) each count 20% towards the course mark.

We use crowdmark to conduct quizzes, problem sets, midterm and final assessments online. You will be asked to photograph or scan your work and upload the resulting pdf file onto the crowdmark servers.

Remarking requests should be submitted (with written justification) within 7 days of when the item in question was returned. Your TA will handle quizzes, and I will handle exam regrading. If you find that you are not satisfied by the outcome then you can make a follow-up request to me. In all cases, bear in mind that a remarking request might raise or lower your mark, or it may remain the same.

If you miss an exam for a legitimate and serious reason, you or someone who speaks for you must email me within twenty-four hours of the exam. In addition, you must submit a hard copy the standard documentation to me within one week of the exam.

Academic integrity statement:   Consult the website Student Academic Integrity for information.