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: PHYS 108

Enriched Physics II

“Oh my God! Something is changing my magnetic flux!”

Text: David Halliday, Robert Resnick and Jearl Walker. Fundamentals of Physics 10th Edition Volume 2 (Chapters 21-44)

Prof: Dr Janis McKenna

Janis keeps things really straightforward. Further, she brings entertaining demo’s to class. She exploded lots of things and showed us how several devices work, ranging from a rail gun to an electric guitar. She is super-passionate about particle physics, and comes to the tutorials to help explain. Discussions on magnetic monopoles are always on the table. She also gave us guided tours of Triumf. Overall, a great prof for an enriched class in electromagnetism.

Difficulty

In comparison to PHYS 107, the professor and the textbook was a lot easier to understand. At the same time, electricity and magnetism is more abstract then mechanics. Further, you are expected to have grasped the basics of calculus by now, so the maths is harder. There was no scaling in this course yet the average was 75-78%, so if you keep up with the material you are okay. They through some tricky tutorial and homework questions at you once in a while, but rarely on exams or midterms. The midterms and exams were fairly conceptual-only a handful of plug-n-chug or mathematical questions. Most of the questions on the exam focused on applying (a) known physics concept/s in a possibly new environment. Thus, the cheat sheet was more of a security blanket than anything else.

Key Concepts

Maxwell’s Equations

Voltage

Electric Fields

Charge

Magnetic Fields

Circuits

Hard Concepts

Induced EMF: Never understood how an EMF can be circular, and not produce a voltage. Just learnt to accept magic.

Inductance: Tricky at first. Helpful to view as capacitance backwards.

Flux: Flux is mentioned in all of Maxwell’s Equations. Important to write flux through a loop as an area integral for some questions.

Integration: Sometimes its difficult to set-up the integral correctly, for a particular current or charge distribution. Important to make good use of trigonometry and right-hand rule. Also, check the answer.

Conclusion

Fun course. Not as much work as Phys 107. Recommend it to anyone who has a vague interest in Physics. Even if you don’t do well, Janis’s demo’s will make it worthwhile for sheer entertainment value.

Course Review: PHYS 107

Enriched Physics I

“In the same way that Calculus was invented for Mechanics, most of Mathematics was invented by physicists”

Text: Matter and Interactions Vol 1, Modern Mechanics 3rd Edition by Chabay and Sherwood

Prof: Dr. Ian Affleck

Google Ian Affleck. He’s got stuff named after him. Physics stuff. He’s a bad-ass.

Dr. Affleck was actually a lot humbler in person then you would expect. He doesn’t talk to his students as if he is an all-knowing-master. The in-class discussions are pretty useful, as are the tutorial discussions. The I-clickers come pretty fast though, so watch out! I lost many participation marks, overly engrossed in a discussion. Quite often during the lectures, there were large chunks of time when I had no clue what the prof was talking about, and neither did my neighbours. Dr. Affleck would sense that he had lost half the class at some point and would ask, optimistically, “Any questions?”. When no-one raised their hand because they could not sensibly articulate their wide-ranging confusion about what was going on, Dr. Affleck would continue, with renewed confidence. At the same time though, when I did my readings thoroughly and did the homework, I noticed that Dr. Affleck boiled down the concepts mentioned in the textbook to a simplicity and tangibility that was really rewarding when I got it, that is.

Difficulty

Not knowing what’s going on happened a lot to me in this class.  The readings are quite challenging and the lectures can be pretty out there. However, thanks to generous scaling, innovative grading and a final exam that focussed a lot more on high-school Physics, one can do quite well in this course. Some of the key concepts in this course are from high-school Physics, just generalized.

Key Concepts

Momentum Principle

Energy Principle

Angular Momentum Principle

Hard Concepts

Entropy: Though I didn’t include it in the key concepts, this is a fundamental concept within Physics and can it take a while to get your head around it

Angular momentum esp. gyroscopes: Angular momentum meets vector calculus for some crazy, yet rewarding Physics

Energy Quantization: Quantum physics can get pretty funky when there are multiple types of energies being quantized. Esp. with a ball-and-spring model of matter.

Collisions: Can involve some tricky geometry and hairy systems of equations

Relativity: Particles may suddenly start travelling at relativistic speeds rendering multiple carefully derived formulae useless. Intuition also fails you.  One has to use first principles.

Lab with Doug Bond and Joss Ives

Not so much Physics as a Statistics course. Not too much pre-lab but some experiments can be pretty repetitive. They attempted to prevent us from collaborating with our lab partners on lab notebooks and spreadsheets but it didn’t really prevent copying.

I suppose I will eventually be grateful for what I learned during those 3-hour chunks, but at this stage my memories are of frustration with Excel and a mercilessly fast learning and implementing speed. The statistical tools you learn are not rigorously proved, in stark contrast to the more theoretical physics class, which could peeve some, but I infer the lab is intentionally meant to be more “hands on”.

Conclusion

Really rewarding course. Could change the way you see the mechanical processes in nature.