ChapterZero

I haven’t done too much this weekend. I read the first of four sections in the chapter on tensors for the geometry course, and predictably got lost in a welter of details and notation. Did I mention the horridness of the official course text? I’m going to do the homework for that section tomorrow– if I find myself lost, I remember a book in the library that covers exactly the same material in a more friendly manner, so I can go reference that.

After some conversations with one of my roomies, an aerospace engineering grad student, I decided to take a look at continuum mechanics, and see if that’s a good choice for my required course external to the applied math department. There are only a few subjects I think would be worth the time and effort at this point in my career, when I should be focusing mainly on my research: analytical mechanics, continuum mechanics and fluid dynamics, relativity, and quantum mechanics. With the exception of relativity and quantum mechanics, these areas are tied to applied mathematics at the hip– a bunch of techniques and the attendant physical intuitions from fluid dynamics have made their way into the collective psyche of applied mathematics, and it’s next to impossible to go a couple of days in our department without hearing about a lagrangian or hamiltonian.

In fact, given the way physics terms– viscosity, stress tensor, lagrangian, boundary layers, advection, shocks, streamlines etc.– (a weak selection, but this is just off the top of my head) are tossed about by our professors, I’m surprised we don’t have a comprehensive physics for applied mathematics course in our department. There’s probably a mathematics of physics course somewhere on campus, but the emphasis in such courses is on applying mathematics to physics problems, as opposed to seeing how physical problems have motivated mathematical techniques and how artificial embeddings of problems in a physical context can assist tremendously in developing helpful intuitions. A subtle but important difference.

As for relativity and quantum mechanics, I just think they’re natural subjects to study. You know, being the two most important physical theories developed in the past century or so. Relativity is to me, one of the sexiest branches of physics, and quantum mechanics seems to be of growing importance in applied mathematics– Schrodinger’s equation seems to be becoming a motivational force in the same way, if to a lesser extent, that the Navier Stokes equations indisputably are. I’ll admit that I base this entirely on my person experiences, seeing a load of papers that somehow trace their motivation back to Schrodinger’s equation. I imagine that someday we’ll teach sympletic integration in our introductory courses on the numerical solution of ODEs.

All of which brings me, in a roundabout manner, to the original reason for this post: a link to the awesomeness that is the National Committee for Fluid Mechanics Films. I’ve only viewed part of the cavitation video (the segment showing the bubbles spun off of a propeller is achingly beautiful), but already I feel like pestering someone in the aero- or mechanical engineering departments to let me see a live hydrodynamics experiment.