ENGR 213 Concordia - Applied Ordinary Differential Equations
ECA Crash Course notes (30/11/2025)
Course Rating
A summary of what how I would personally rate the course based the following metrics. How I rate can be different from how you view it. Everyone learns differently.
| Metric | Rating |
|---|---|
| Course Complexity | ▮▮▮▯▯ (3/5) |
| Lecture Attendance Importance | ▮▯▯▯▯ (1/5) |
| Industry Relevance | Degree dependent |
| Exam Difficulty | ▮▮▮▮▯ (4/5) |
| Self-Study Suitability | ▮▮▮▮▯ (4/5) |
If you're looking for the tutoring link, sorry! I don't tutor this course anymore.
Topics
Generally, the topics are the same every year. However, content covered may differ depending on your professor.
When I took the course back in 2023, the topics included:
Note, the numberings correspond to the textbook chapter (see below for textbook)
- 1. Differential Equations and Their Solutions
- 1.1 Definition and Terminology
- 1.2 Initial Value Problems
- 1.3 Differential Equations as Mathematical Models
- 2.1 Solution curves without a solution
- 2.2 Separable Equations
- 2.3 Linear Equations
- 2.4 Exact Equations, integrating factors
- 2.5 Solutions by Substitution (Bernoulli, homogeneous, linear substitution)
- 2.7 Linear models (growth/decay, heating/cooling, circuits, mixtures)
- 2.8 Non-linear models (Population dynamics, logistic equation, leaking tank)
- 3. Higher-Order Differential Equations
- 3.1 Theory of Linear Equations
- 3.3 Homogeneous Linear Equations with Constant Coefficients
- 3.4 Undetermined Coefficients
- 3.5 Variation of Parameters
- 3.6 Cauchy Euler Equations
- 3.7 Nonlinear Equations, Reduction of Order
- 3.8 Linear Models. Initial Value Problems (mass-spring systems, free motion)
- 3.8 Linear Models. Initial Value Problems (driven motion and LRC-circuits)
- 5. Series Solutions of Linear Equations
- 5.1.2 Power Series Solutions
- 10. Systems of Linear Differential Equations
- 10.1 Theory of Linear Systems
- 10.2 Homogeneous Linear Systems
- 10.4 Non-Homogeneous Linear Systems
- 17. Complex Numbers
- 17.1 Complex numbers
- 17.2 Powers and Roots
The course followed the textbook "Advanced Engineering Mathematics, by Dennis G. Zill and Warren S. Wright, 7th Edition".
How to study
- Depending on your learning style and prior knowledge of the concepts above, this is a subject that can almost fully be self-taught.
- Learn the content through your professors slides or notes and the following youtube channels: The Math Sorcerer, Professor Leonard.
- Work through textbook practice problems, tutorial questions and past papers.
- The key to getting a good grade is to just solve a bunch of past papers. The key to actually being proficient is to truly understand what you are doing when solving each question.
- I cannot share past papers here however, I believe you can find some online.
The final exam
- From my experience, the final exam will almost certainly be at least 70% similar to past papers with some variations depending on your professor. In general, all you need to do to succeed is to be able to solve at least 3 past papers comfortably by yourself before going into the final.