Ordinary Differential Equations - Differential Equations | Arts and Science ONLINE

Ordinary Differential Equations

MATH 225/3.0

An introduction to solving ordinary differential equations. Topics include first order differential equations, linear differential equations with constant coefficients, Laplace transforms, and systems of linear equations.

Please note: This course is typically offered in the summer term

Learning Outcomes

Learning Outcomes

  • Creating differential equations from word problems/application scenarios.
  • Choosing the most appropriate method for solving a specific boundary value or initial value problem from among several different viable techniques. 
  • Generating general and particular solutions to differential equations using appropriate solving techniques.
  • Verifying that an expression or function is actually a solution to a differential equation.
  • Interpreting the results of a differential equation solution.


  • Separable 1st order DEs 
  • Linear 1st order DEs
  • Higher-order linear DEs with constant coefficients
    • homogeneous - real distinct roots, complex roots, repeated real roots.
    • non-homogeneous - overlapping and non-overlapping with the homogeneous solutions.
  • Laplace Transforms 
    • Introduction to Laplace as an integral transformation, change in domain from t to s.
    • Forward and backwards Laplace transforms of functions using table of transforms.  New functions: piecewise/step functions. 
    • Forward and backwards transformation of DEs using Laplace transforms
  • Systems of differential equations
    Background/review - row reduction, computing eigenvalues and eigenvectors of matrices
    • Transforming systems of 1st order DEs into matrix form.
    • Building vector solutions to matrix form using eigenvectors and eigenvalues.


Introduction to ordinary differential equations and their applications to the natural and engineering sciences.  Specific topics include first order differential equations, linear differential equations with constant coefficients, Laplace transforms, and systems of linear equations.

This course may be used by Queen’s students towards the degree requirements of programs in Arts & Science (except for MATH majors).  Students from other institutions pursuing engineering or science programs should check with their home institution regarding the suitability of this course towards their degree programs.

NOTE: Some knowledge of linear algebra is assumed.


Course Resources


SOLUS is Queen’s Student On-Line University System. You’ll have access to a SOLUS account once you become a Queen’s student. You’ll use SOLUS to register for courses, add and drop courses, update your contact information, view financial and academic information, and pay your tuition.

About OnQ

onQ is Queen's online learning platform. You'll log into onQ to access your course. All materials related to your course—notes, readings, videos, recordings, discussion forums, assignments, quizzes, groupwork, tutorials, and help—will be on the onQ site.

About Credit Units

Queen’s courses are weighted in credit units. A typical one-term course is worth 3.0 units, and a typical two-term course is worth 6.0 units. You combine these units to create your degree. A general (three-year) BA or BSc requires a total of 90 credit units.

Computer Requirements

To take an online course, you’ll need a high speed internet connection as well as a microphone and speakers to be able to watch videos, hear sounds, and participate in interactive online activities. A webcam is recommended but not necessary.

System Requirements:

Computer Specifications

  • Windows 8.1 or newer
  • OSX 10.13 (High Sierra) or newer
  • Dual Core 2 GHz processor
  • 4 GB RAM
  • Soundcard
  • USB Headset
  • Webcam

Supported Browsers

  • Chrome (preferred - latest version)
  • Firefox (latest version)
  • Safari is not recommended as it causes several known issues in onQ
  • Edge is not recommended as it causes several known issues in onQ

Internet Connection

  • Wired high speed access: Cable or better
  • Wifi is not recommended


  • Latest version

Media Player

  • Flash (latest version)

Adobe Reader

  • Latest Version


The deadlines for new applications to Queen’s Arts and Science Online courses are in our Upcoming Application Dates section.

Grading Scheme

The information below is intended for undergraduate students in the Faculty of Arts and Science. Academic Regulations in other Faculties may differ.

Letter Grade Grade Point

GPA Calculators
Have your SOLUS grade report handy and then follow the link to the Arts and Science GPA calculators.

How does this affect my academics?
See the GPA and Academic Standing page.

Follow the link above for an explanation of how the GPA system affects such things as the Dean’s Honour List, requirements to graduate, and academic progression.

Frequently Asked Questions on the Grading Scheme
Please follow this link to the FAQ's

Tuition Fees

Tuition fees vary depending when you start, your year, faculty, and program. Fees for Summer Term 2018 first-year Distance Career Arts & Science Domestic students are as follows: for a 3.0-unit course, $685.90; for a 6.0-unit course, $1371.80 See also Tuition and Fees.

Campus Bookstore

All textbooks, if required, can be purchased at Queen’s Campus Bookstore.

Non-Queen’s Students

All Queen’s Arts and Science Online courses are open to students at other universities. Before applying as a visiting student, request a Letter of Permission from your home university that states that you have permission to take the course and apply it to your degree. See also Apply.

Academic Integrity

Please see Queen’s policy statement on academic integrity for information on how to complete an online course honestly.