Honours Differential Calculus
“For any topic in mathematics, you just need to do a few ‘cute’ problems. Otherwise, your mind starts ‘turning'”
Text: Robert A. Adams and Christopher Essex: Calculus: Single Variable, 8th Edition, Pearson, Toronto, 2013.
Prof: Dr. Yue-Xian Li
The thing that I’ll remember the most from Dr. Li’s class were his bizarre one-line quips including:
“You should have asked me that question weeks ago! You are going to fail the midterm tomorrow!”
“How can you confuse a “gamma” with an “r”? The “gamma” looks like the thing you use to hang people!”
“I have some videos I could show you… people driving on a bridge while it is collapsing… some really great videos”
“There is some theory behind this, but I don’t really understand the theory… let me show you how to get the solution though”
“My third-year students keeping making this mistake, but you guys are honours, so you shouldn’t have a problem”
Dr. Li is actually a mathematical biologist. He was alots of fun and very passionate. He was also really nice during office hours. The best part of his classes were when he deviated from the textbook a bit. That said, he took most of his examples directly from the assigned readings in the textbook.
Difficulty
I am sure most people who takes this class are a bit apprehensive about the word honours. Is that apprehension justified? I am not so sure. I think that the key to this course is identifying the handful of additional/challenging concepts early on, and being prepared to put some extra effort into them. Both the midterms and the final were really fair, since the prof gave us very similar practice exams. I found the last few questions on the weekly homework pretty hard, though. I often had to think over the questions for a few days to understand them. I also tripped on an optimization question in the final, but I think that was just me…
Key Concepts
Limits
Derivatives
Mean-Value Theorem
Continuity
Hard Concepts
Epsilon-delta Definition of Limit: Arguably the hardest concept to understand quickly in the course. Make sure you understand the “logic” of it before diving into the math.
Proofs: Proofs often involving mean value theorem on tests, but anything course-related for homework.
Differential Equations: Lots of Physics often involved, could be hard if that’s not your strongest subject.
Derivatives of inverses: Some of these questions can be computationally difficult and you can get really confused if you don’t notice that a function evaluated at its inverse is x.
Continuous and Differentiable Functions: Often involving piecewise functions with parameters. Its best to go back to definitions when dealing with either or both of these properties.
Chain rule: If you don’t like computation, some chain rule questions could bring you down. Its just a matter of practice and accuracy though. Not really smarts.
Optimization and Related Rates; If geometry’s not your strongest point, these could be a challenge. Once again, practice is key. ( I didn’t practice optimization enough for my final)
Conclusion
Great course, but be prepared to put in extra effort.
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