ENGR 233 Concordia - Applied Advanced Calculus
Course Rating
A summary of what how I would personally rate the course based the following metrics.
| Metric | Rating |
|---|---|
| Course Complexity | ▮▮▮▮▮ (5/5) |
| Lecture Attendance Importance | ▮▮▮▯▯ (3/5) |
| Industry Relevance | Degree dependent |
| Exam Difficulty | ▮▮▮▮▮ (5/5) |
| Self-Study Suitability | ▮▮▮▯▯ (3/5) |
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Topics
Generally, the topics are the same every year. However, content covered may differ depending on your professor.
When I took the course in 2025, the topics included:
Note, the numberings correspond to the textbook chapter (see below for textbook)
- Vectors
- 7.1 Vectors in 2-space
- 7.2 Vectors in 3-space
- 7.3 Dot product
- 7.4 Cross product
- Lines, Planes, and Vector Functions
- 7.5 Lines and planes in space
- 9.1 Vector functions
- Motion and Curvature
- 9.2 Motion on a curve
- 9.3 Curvature. Components of Acceleration
- Partial and Directional Derivatives
- 9.4 Partial derivatives
- 9.5 Directional derivative
- Planes, Lines, Curl, and Divergence
- 9.6 Tangent planes and normal lines
- 9.7 Curl and Divergence
- Midterm break
- Line Integrals
- 9.8 Line integrals
- 9.9 Independence of path
- Double Integrals
- 9.10 Double integrals
- 9.11 Double integral in polar coordinates
- Green’s Theorem
- 9.12 Green’s theorem
- Surface and Flux Integrals
- 9.13 Surface/flux Integrals
- Stokes Theorem
- 9.14 Stokes theorem
- Triple Integrals
- 9.15 Triple Integrals
- Divergence Theorem
- 9.16 Divergence theorem
- Change of Variables in Multiple Integrals
- 9.17 Change of variables in multiple integral
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 - with A LOT of effort.
- Learn the content through your professors slides or notes and the following youtube channel (all my notes are a taken from his youtube recorded lectures): Professor Leonard.
- Work through textbook practice problems, tutorial questions and past papers.
- I personally solved the problems by Professor Leonard and then directly, solved the exam questions corresponding to the topic from the sample exam paper.
- The key to getting a good grade is to truly understand what you are doing when solving each question. This is NOT a course where you can easily cram past papers and be comfortable with getting a good grade.
- 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 60-80% similar to past papers with some variations depending on your professor. Unlike ENGR 213, this is a course that requires a lot of time, commitment and understanding to pass with a good grade. As I've mentioned above, you cannot easily cram and solve past papers. Professors usually test you on each topic with the hardest possible question, so be well prepared.