MAT 267 University of Toronto, Winter 2021
 

MAT 267H1S 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 (log onto Quercus or write to me for the zoom links)
Office hours TBA (Fridays)
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, and a few some applications. These provide the viewpoint needed to enter into the arena of nonlinear dynamics and dynamical systems. The book does not contain some of the analytical material that you will need in subsequent courses in geometry, analysis, and PDE. For this reason, additional material will be provided when needed.
  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.
  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. Global nonlinear techniques. Gradient systems, Hamiltonian systems.
  8. Closed orbits and limit sets.
  9. Applications in Geometry, Physics, and Biology.
Schedule
Evaluation:
  • Homework.   8-10 problems per week. Please discuss freely!
  • Quizzes.  Once-a-week short quizzes based on one homework problem (in tutorial). Quizzes will be marked 0, 1, 2.
  • Midterm Assessments.   February 9, March 16 (both Mondays)
  • Final Assessment.  TBD (between April 13 and 23).
Marking Scheme: The course mark has 5 equal parts: Quizzes (drop 2), Midterm 1, and Midterm 2 each count 20%, Final Assessment 40%.

We will be using crowdmark to mark the quizzes, midterm and final assessments. You will be asked to photograph or scan your work and upload the resulting pdf file onto the crowdmark servers. Should you feel that your homework or exams have been misgraded, then you must submit a request for regrading (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. Go to https://fas.calendar.utoronto.ca/ term-work-tests-and-final-exams for instructions and more information.

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