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
Summer (May–July) 2025
Course Dates
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Exam Dates (if applicable)
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Delivery Mode
Online