The education students receive here at Linfield is not your average, run of the mill college degree. By no means is this the first time that I’ve had this realization or come to this conclusion; instead, I’ve had a number of experiences show me this is true (see here and here for some examples). This morning’s lecture in my Partial Differential Equations (PDEs) class served as yet another reminder of the quality of a Linfield education. Last week we finished developing our method for solving examples of the heat equation seen in Chemistry and Physics. This is a differential equation that models heat distribution and flow over time. My professor, Dr. Steve Bricher, told us today that the method we had been learning about and using on smaller problems, and now the heat equation, was something he didn’t see until his third year in Graduate School! I was pretty shocked. I knew I was taking a high level class, but I didn’t realize we were covering topics that most undergrads never even see. Today we learned the usual approach to solving PDEs at the undergraduate level, which is much simpler but can only handle special cases. As expected, the solutions came out to be the same, but this time, knowing that we took the easy route, the solution was much less satisfying. It wasn’t something that built upon the entire semester’s worth of knowledge we have developed, instead it was something we easily could have done the first day of class as it only used concepts seen in prerequisite courses. Of course this came at a cost of only being able to solve specific types of equations instead of all equations. I don’t think it was Steve’s intention to show us how much more in depth our class was compared to a regular differential equations class, but that was the message I took away from today’s lecture. In short, most undergraduate differential equations classes use a much simpler method to solve PDEs, but this method only works for a small amount of equations of a very specific type. In our class, we have developed a method that will solve any PDE that could ever be conceived, using graduate school level ideas from math. Now I’d say that’s some pretty cool stuff! This is just one example of many that shows the quality of a Linfield education. This quality is found in each department, professor, and class on campus, and it is one of the things that really separates Linfield from the rest of the competition.
Til next time,