MAT 244 Introduction to Ordinary Differential Equations

Fall 2019: Course outlines



2019-2020 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.



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; so, better to buy or to lease the larger one. BVP for ODE are usually addressed in PDE (Partial Differential Equations) class). Also there are different editions available.

We support both editions publishing on Quercus all home assignments; 11th is preferable (cleaner interface for online version), but do not pay premium if you can get 10th. Actually you can use even earlier editions, especially 9th.


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

Learning Resources

This class in the previous years (as I taught)

Other Resources

Tests 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 Tests

Missing Quizzes

Doctor's Note

Final Exam


Everything (Tests, Final Exam, Quizzes) are graded using Crowdmark. Please read here. It also covers the Lost work/mark issue.


All right-pointed triangles (►) are expandable (click on them!) and down-pointed triangles (▼) are collapsable