# Course Review: MATH 215

Elementary Differential Equations I

“UBC is a very progressive place…Because you get to learn Linear Algebra before Differential Equations!”

Text: Notes on Diffy Qs: Differential Equations for Engineers, by Jiri Lebl

Prof: Dr Dan Coombs

Dr Dan Coombs has great British accent, and a wry sense of humour which helps to keep interest in the class. He tries to balance between tolerating conceptual questions and making progress in the more recipe-oriented curriculum. He spent a lot of effort restructuring the curriculum to be based on Linear Algebra, so as to make the class more conceptual and slightly less “formula-up-my-sleeve” math, though it still is.

Difficulty

The homework is really exhausting. The hand calculations have awful numbers in them, making them really tedious. The Matlab is … Matlab. As a CS student I thought Matlab would be a breeze, but that was not the case, as the language has a lot of quirks. The number of questions in a homework set is a lot considering the time each one takes. With the exception of the first homework, where we were given real world problems and had to come with models for them, I didn’t feel I got a lot out of the homework, except learning a few random facts about Matlab after trial and error.

Key Concepts

Modelling nature as a differential equation

First order linear equations

Linear systems of differential equations

Laplace transform

Non-linear systems

Hard Concepts

Partial fractions: Thought they were pretty easy, but had a really gross one on the final

Non-linear classification of fixed points: Can get a bit confused between different fixed points

Classification of 2nd order linear systems: If you don’t want to re-derive them, need to be able to recall them quickly.

Conclusion

Homework was a schlep. Interesting topic, but recipe-driven curriculum almost kills it. IMHO, focus should be modelling natural phenomenon. The problem with the recipe driven approach, even for non-math students, is that (1) Engineers will probably just use Wolfram/computer system to solve it anyway. (2) While it might be helpful for them to classify what can/cannot be solved etc, odds are if it is non-linear you will try your luck, or use a linear approximation anyway.

# Course Review: MATH 227

Text: (none)

Prof: Dr. Joel Feldman

Dr. Joel Feldman strikes a great balance between being really organized, while still pretty relaxed. He is very helpful, in that he is always available between classes for questions. He is also really knowledgeable about the field (as he is a mathematical physicist) which is great, though he did give us a particularly tragic expression when we said we didn’t know what curl was, halfway through the course and he had to explain it.

Difficulty

The weekly assignments are generally all straightforward. The questions vary from computational to small proofs. I missed the first midterm, but a lot of people got wrecked, and it looked tough so watch out. Each question in the second midterm was manageable, though it required thinking. The challenge is that there are only four questions, so the cost of getting one question completely wrong is quite high. The final was similar except it had more questions. The challenge then was that often it was not clear which of the various techniques we had learned in the course was the correct approach to a question.

Key Concepts

Analysing/ parameterizing curves in 2,3-space

Analysing/ parameterizing surfaces in 3-space

Analysing/ parameterizing vector fields in 3-space

Integrating over curves, vector fields, and surfaces

Integral Theorems

Hard Concepts

Applications of integral theorems: Hard to pick the right strategy that is going to work.

Biot-Savart Law: Really abstract, not sure if I understood it.

Conclusion

Feels like a fun physics course. Wish we had more time to discuss differential forms, but other than that pretty interesting class.

# Course Review: MATH 120

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.