Department of Mathematics

University of Toronto

MAT244 Introduction to Ordinary Differential Equations

Spring of 2018

Course outlines



2017-2018 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.


William E. Boyce, Richard C. DiPrima, Douglas B. Meade.
Elementary Differential Equations and Boundary Value Problems, Enhanced eText, 11th Edition

In Canada it is available as electronic resource only; printed editions (hardcover or paperback) are not available (unless by premium price). Meanwhile 10th Edition is out of print.

There are two different books ("with Boundary Value Problems" and without them; the second one is simply a shorter version but it costs the same; BVP for ODE are usually addressed in PDE (Partial Differential Equations) class).

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. Home assignments will use numbers from the textbook. This makes older editions unusable for home assignments.


We will cover (in full or partially) chapters 1, 2, 3, 4, 5, 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.

Learning Resources

This class in the previous years (as I taught)


  • WolframAlpha
  • ODE Plotters

    Tests and Quizzes


    There will be early/late sittings (TBA).


    We plan to give 7 Quizzes drawn from the Home Assignments, 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 ponts 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 and Quizzes.

    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,


    Missing work