# Ordinary Differential Equations

MTHE 225/3.5

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

## 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.

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.

## Description

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.

## Terms

Summer 17: May - July
Course Dates:
May 1 - July 21, 2017
Exam Dates:
July 25 - 28, 2017

## Evaluation

 Fundamentals Online Self-Test 2% Online Homework (weekly) 10% 3 Tests 23% Modelling Assignments (includes peer assessment) 10% Weekly Check In 5% Proctored Final Exam 50%

**Evaluation Subject to Change**

### Final Examination

Students must write their exam on the day and time scheduled by the University. The start time may vary slightly depending on the off-campus exam centre. Do not schedule vacations, appointments, etc., during the exam period.

## Instructor

Professor Alan Ableson (ableson@mast.queensu.ca)

## Time Commitment

To complete the readings, assignments, and course activities, students can expect to spend on average, about 120 hours on the course.

### 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.

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.

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:

• Laptop or Desktop computer purchased within the last 5 years. (mobile devices are not supported)
• Windows Vista SP2/Mac OSX 10.9 or higher
• Up to date versions of Firefox, Internet Explorer or Safari. Please note that Google Chrome is not recommended for use in our courses.

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

#### Tuition Fees

Tuition fees vary depending when you start, your year, faculty, and program. Fees for Summer Term 2017, Fall Term 2017 and Winter Term 2018 first-year Distance Career Arts & Science Domestic students are as follows: for a 3.0-unit course, \$666.91; for a 6.0-unit course, \$1333.82. See also Tuition and Fees.

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 A+ 4.30 A 4.00 A- 3.70 B+ 3.30 B 3.00 B- 2.70 C+ 2.30 C 2.00 C- 1.70 D+ 1.30 D 1.00 D- 0.70 F 0.00

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.