Overview
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.
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.
Topics
- 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.
Terms
Evaluation
2% - Fundamentals Online Self-Test
10% - Online Homework (best 10 of 12 weekly)
24% - Tests (x3)
10% - Modelling Assignments (Includes peer assessment)
4% - Weekly Check-in (best 10 of 12 weekly)
50% - Proctored Final Exam
**Evaluation Subject to Change**
Proctored Exams
Exam Centre Location, Eligibility, and Fees
Students enrolled exclusively in online courses may choose one of two options to write this course’s proctored assessments:
- You may choose to write the assessments online under supervision of Examity proctoring services. A $100 fee will be charged to your SOLUS account. This fee is known as the Off Campus Exam Admin Fee and is applied in SOLUS at the earlier of: term tuition posting date, or the date at which exam writing method is changed to online. The fee is assessed once per ASO course with proctored assessments.
- You may choose to write the assessments in-person on Queen’s campus in Kingston at no additional charge.
Students enrolled in at least one on-campus course are expected to write this course’s proctored assessments on-campus during the scheduled exam time. They will not be permitted to write this course’s proctored assessments online.
Students were prompted to indicate their preferred exam writing method when enrolling in the course in SOLUS. The exam writing method may be changed by contacting the ASO Exams Team at aso.exams@queensu.ca.
Information for students writing online assessments using Examity
Selected assessments in this course will be administered in onQ using online proctoring provided by Examity, a third-party, cloud-based service. This proctoring solution was chosen to support our efforts in maintaining academic integrity when online proctoring is required. Queen’s has conducted an extensive privacy and security review of Examity and has entered into a binding agreement with terms that address the appropriate collection, use and disclosure of personal information in accordance with Ontario’s privacy legislation. To learn more about online proctoring, please see the information provided by the Office of the University Registrar.
If you registered to write online with Examity, all information pertaining to the technical requirements and preparation for writing online will be posted in onQ well in advance of your exam. 
The use of Examity as described is unique to courses offered by the Faculty of Arts and Science Online. Other Faculties use online proctoring solutions in different ways under different regulations. Students should contact the appropriate Faculty examination team if they have questions.
Timing of Final Examinations
The exam period dates for each Term are listed on the Faculty of Arts and Science webpage under "Important Dates". Student exam schedules for the Fall Term are posted to SOLUS immediately prior to the Thanksgiving holiday; for the Winter Term they are posted on the Friday before Reading Week, and for the Summer Term they are individually noted on the Arts and Science Online syllabi. Students should not make any travel plans until after the examination schedule has been posted. Exams will not be moved or deferred to accommodate employment, travel/holiday plans or flight reservations. Students experiencing extenuating circumstances preventing them from writing their exams as scheduled should review the information about the Academic Consideration process.
Textbook and Materials
ASO reserves the right to make changes to the required material list as received by the instructor before the course starts. Please refer to the Campus Bookstore website at to obtain the most up-to-date list of required materials for this course before purchasing them.
Most learning materials (notes, practice problems, etc.) will be supplied as part of the course.
Calculator Policy
Calculators acceptable for use during quizzes, tests and examinations are intended to support the basic calculating functions required by most Arts and Science and Applied Science courses. For this purpose, the use of the Casio 991 series calculator is permitted and is the only approved calculator for this course. This calculator sells for around $25 at the Queen's Campus Bookstore, Staples and other popular suppliers of school and office supplies ().
Time Commitment
To complete the readings, assignments, and course activities, students can expect to spend on average, about 120 hours on the course.