Department of Mathematics

University of Toronto

MAT244 Introduction to Ordinary Differential Equations

Fall of 2018

Course outlines



2018-2019 Timetable Description

First order ordinary differential equations: Direction fields, integrating factors, separable equations, homogeneous equations, exact equations, autonomous equations, modeling. Existence and uniqueness theorem. Higher order equations: Constant coefficient equations, reduction of order, Wronskian, method of undetermined coefficients, variation of parameters. Solutions by series and integrals. First order linear systems, fundamental matrices. Non-linear equations, phase plane, stability. Applications in life and physical sciences and economics.


In comparison with 10th Edition, 11th has an additional author. Usually the main difference between edition is that the problems are shuffled; so their numeration differ. We support both editions (on Quercus); 11th is preferable.


We will cover (in full or partially) Chapters 1, 2, 3, 4, 7 and 9:
  1. Introduction
  2. First-Order Differential Equations
  3. Second-Order Linear Differential Equations
  4. Higher-Order Linear Differential Equations
  5. Series Solutions of Second-Order Linear Equations (?)
  6. The Laplace Transform
  7. Systems of First-Order Linear Equations
  8. Numerical Methods
  9. Nonlinear Differential Equations and Stability
  10. Partial Differential Equations and Fourier Series
  11. Boundary Value Problems and Sturm-Liouville Theory

Note: Chapter 5 will be covered (if at all) at the very end of the course, if the time permits.

Learning Resources

This class in the previous years

This class in the previous years (as I taught)

External resources

  • WolframAlpha

  • ODE Plotters

    Tests and Quizzes


    Notes: Later we will schedule early sittings.

    We plan to grade Tests and the Final Exam using Crowdmark. Details will be available later.


    We plan to give 7 Quizzes, each worth 4 points, worth together 20 points. They will be offered either on the Lectures, or on Tutorials (the arrangements could differ for different quizzes).
    If we reduce the total number of quizzes to 6, each will be 5 points worth.

    Home assignments are neither submitted nor graded but Quizzes will be drawn from Home assignments which are due, Quizzes are usually biweekly and are 15—20 min long in class time, see Lecture Notes which cover also Home assignments, Quizzes and Handouts.

    Marking scheme

    Your Final Mark will be computed as follows: \begin{gather*} \mathsf{FM}= \min\bigl[ \mathsf{Q} + \mathsf{BM}+\mathsf{T}_1 + \mathsf{T}_2 + \mathsf{FEM},\, 100\bigr],\\[3pt] \mathsf{Q} = \mathsf{Q}_1 + \mathsf{Q}_2+\mathsf{Q}_3 + \mathsf{Q}_4 + \mathsf{Q}_5 + \mathsf{Q}_6 + \mathsf{Q}_7 \qquad \text{with 2 worst Quizzes dropped} \end{gather*} where $\mathsf{FM}$ and $\mathsf{FE}$ are your Final Mark, and the Final Exams Mark respectively,



    Your subject line should start from MAT244 and include the subject of the email. Do not respond to the unrelated emails (or if you do, change the subject line). Email should contain all necessary information, including your Lecture Section and Tutorial Section (if needed).

    Missing work

    If you missed some Test or Quizzes

    Lost work/mark

    Your Test/Quiz paper is missing; mark is wrong or missing