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.
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