meanfreepath | (no subject)

So there exists a Princeton essay. I don't know how good it is yet, but hopefully it will get to good soon.

Man, I really should have taken Real Analysis this semester and then take Complex next spring. There's just soooo much math I don't know well enough. For plasma physics, one must absolutely know complex variables well, in addition to tensors. I never understood tensors when we did them for half a week in Physics 50... it's not that difficult to understand some tensors like a pressure tensor or an inertia tensor, but when it comes to contravariant/covariant and transformations that involve tons of pushing subscripts around and the annoying Einstein summation convention of automatically summing over repeated indices... Why oh why didn't I double major in math and physics?

Other thing I don't know anything about: classical perturbation theory. Indeed, I remain totally ignorant of such important topics as a formal theory of Poisson brackets, action-angle variables, and Hamilton-Jacobi theory. Princeton's plasma program requires a course on asymptotic methods that largely focuses on limiting solutions to nasty differential equations, such as the horribly nonlinear ones arising in plasma physics, things like perturbation theory, classical WKB theory, and boundary layer theory. A course on advanced math methods would be so much more useful than computational physics... Perhaps I should sit down this summer and work through Arfken and Weber, as well as Hand and Finch to bring my weak background in classical mechanics up to snuff.

In other news, I found out while walking in Philly Chinatown with

nightengalesknd this afternoon that PFD still carries 50 foot Bangor ladders. This makes sense, given the narrow alleys one will find in Philly. I've always wanted to learn how to raise one of those ladders, which requires the use of staypoles. Such ladders, however, are of limited utility in suburbia; we don't carry them (nor, to the best of my knowledge, do the companies we run with), and they don't even teach them in fire school. The Bangor ladders, while cool, are heavy (close to 200 pounds, I think) and are manpower intensive, requiring 5 or 6 people to raise. Yes, when one has the space to park an aerial ladder truck or tower ladder, those are much nicer. But there's something about Bangor ladders that just brings back the days of yore...

Flat | Top-Level Comments Only

Arfken is graduate level. Like, same level as Jackson. No one expects you to know that coming in. And Marion and Thornton is a normal amount of classical mechanics to know coming in--it'll actually be more rigorous than some people's backgrounds, and the same as everyone else's.

As far as I know, Poisson brackets work the same way as commutators, only on classical matrices rather than quantum mechanical ones.

You know more of this stuff than you think, and the rest of it (most of it, really) you probably aren't expected to know coming in. For example, most of my friends barely had any exposure to covariant/contravariant notation as undergrads, either (the only reason I did was because I took GR). It gets taught. You really aren't expected to know everything.

Really. You worry too much. Your education isn't lacking (although if you don't know complex analysis, you might want to take it ASAP--I got through without it, but I'm also an experimentalist in a branch of physics that doesn't really need it).

I know Princeton teaches Goldstein to their sophomores, and Cornell, uses Hand and Finch (Lou Hand happens to be a Swattie, by the way), which does cover some of the more advanced stuff not in T/M.

Everyone seems to use Goldstein other than Swat, actually. I never found it to be a problem.

Does the more advanced stuff actually get covered? Because I know we got farther in T/M than some schools do.

Again, you worry too much. I'm sure Caltech does something more advanced, too, and MIT teaches Jackson to undergrads. That doesn't mean that that's where most of your classmates will be; the ones who are will probably get to skip of some of the beginning graduate classes, but the classes certainly won't be geared toward them.

Have you seen the lobby of 2 Liberty Place? They have the first steam powered fire engine in America on display.

I second what

sildra said. They will teach what you don't know, and there will be many other students in the same boat as you. There will be people who are better prepared mathematically, it's true. But it's not something for you to stress over. Covariant and contravariant matrices aren't too difficult to grasp, and in my experience, I got so much practice pushing subscripts around in Einstein notation in grad school that it didn't matter that I'd never really used it as an undergrad. (And trust me, the Einstein convention is NOT annoying! It's darned useful! Who wants to write out that many sums?)

I had my undergrad mechanics course out of Marion Thornton, and I found my classical mechanics preparation to be much better than many of my classmates (we covered Hamiltonians in that class, many of my classmates hadn't seen a hamiltonian, and the Hamitonian equations of motion, before grad school (at least in the context of mechanics). I don't know how far you got at Swat, but I wouldn't be to worried about it.)

Princeton eh?