Reflections on Second Semester, Part I

This is the first of four posts looking back at the semester that just ended. The posts will be split up by class or activity. This post focuses on two of my four classes, Partial Differential Equations (PDE) and Waves.


Partial Differential Equations
PDE was without question my favorite class this semester. After first semester, I really missed math, so having a math class made me happy. I grew up hearing "Solve PDE!" said excitedly (math-y family!), and solving PDEs this semester was exciting. We mainly looked at the wave and heat equations, starting on an infinite line and then moving to finite domains. I'd seen some of the finite cases before without the context of the infinite cases, and knowing what happened in the infinite case definitely helped me understand the finite solutions better, particularly with the wave equation. I learned more in PDE than in any of my other classes this semester, and I also found more that I want to learn. For my final project I studied shock waves, and there are extensions/generalizations of the equations I studied that I didn't have time to write up. Aaron, the professor, also mentioned looking at PDEs on graphs at one point, and since I love graph theory, that would be awesome.

PDE was also my most mechanical engineering-ish class (even though it was all math). PDE is one of three math class options for mechE majors, so the class was full of mechEs. That was sometimes a little odd for me; enough of my background is in math that I wasn't often thinking like an engineer, and lots of the other students were. Thermodynamics and fluids are two of my favorite topics within mechE, and even if in practice engineers don't have to directly deal with the partial differential equations, they're there, and I really enjoyed learning about them.

There are definitely times during the semester at which I wish I'd put more time into PDE, but I'm happy with my work, and the class brought me a lot of joy.

Waves
Waves is really best defined by its professor, Sanjoy. His classes tend to have low out-of-class workloads, in-class final exams, and assignments graded on effort. He loves approximation, and whether you intend to or not, you'll pick up some approximation tricks along the way in any class with him.

Waves was my Physics Foundation course. Most of the course was actually about springs because we built our model for a wave out of a system with lots and lots of masses and springs in series. I was familiar with the physics of simple spring systems, pendulums, and waves, but I still learned a lot. I hadn't done enough with multiple mass, multiple spring systems to think much about normal modes of oscillation, which was a focus on the class. Sanjoy also really emphasized that waves are everywhere, so we did a lot of really interesting example problems. Sanjoy also related various areas together, so we ended up talking a little bit about thermodynamics and elasticity, both of which I really like.

The class was a mix of lecture and discussion. Sanjoy lectured, but he regularly gave us problems to work on together in the middle of class, and then we would talk about the problems as a group. This is where I most wish I had done something differently in Waves. Even at the end, I was comfortable working with only a few of the people in the class, so I wish I had moved around a bit more to work with different people

Waves was supposed to focus on music, and we did start with music and get back to it at the very end, but in a lot of ways we ran out of time and didn't do much physics of music. I don't think that took away from the class, though, because music was really just going to be the predominant example, and in general I thought the examples we did, both musical and non-musical, were interesting and appropriate to the topics.

The class definitely taught physics (and linear algebra), but I learned more from being exposed to new ways of thinking or working problems. I'm more likely to look around and see systems as springs or waves (which is often pretty useful, because we know how to deal with springs), and I've picked up some of Sanjoy's problem solving habits. On the final Waves exam, instead of just immediately throwing math at problems (which is definitely my instinct), I thought more qualitatively first, and I also tried to get insight from dimensional analysis, which are both strategies that Sanjoy encourages. Waves wasn't what I was expecting at all, but I'm glad I took it!