First Post

Well, here I am posting on yet another blog. Hello world! f1r2t p0st! Digg me! And with that out of my system, I move on.

So in case it wasn't extraordinarily obvious from my oh-so-creative blog title, I'm Ben Preskill. And I'm a junior at Harvey Mudd College with majors in Math and Physics and a concentration in Economics.

Truth is, I like math. All of it. And I especially like applications of math to cool problems. But I have no idea which applications excite me the most. My solution? Try as many as I can. Fluid mechanics has to be one of the most prominent areas of applied math out there. It's used as a paradigm for applications of calculus, differential geometry, and PDEs, and so I figured I damn well ought to see what this stuff is all about. That's pretty much why I'm taking Continuum and Fluids. Oh, and tensors rock.

Really, I don't know what to expect. I know there are tensors involved and I know we'll be modeling...well, fluids. But that's sort of the point - I don't know anything about fluid mechanics, really, and I want to know what the subject is all about. Moreover, I've seen a lot of math from a physics perspective (being a physics major,) but haven't seen as much physics from a math perspective. Although I don't expect the whole course to be the latter, I'm guessing I'll get a taste of it. Finally, I imagine continuum mechanics makes modeling almost any type of macroscopic physical situation a lot more feasible. That's just a guess, though. For all I know, you might mostly end up with some god-awful system of PDEs that requires ode15s because it's too damn stiff, and then MATLAB takes an hour to spit out a vector containing a bunch of numbers to the negative fiftieth power. But I hope not.

Now, I've been asked about a favorite equation, and I've not put a lot of thought into this. The physicists would love me if I said Schroedinger or a Hamiltonian System. But then, I'm so tempted to pick something powerful and abstract from math, like some kind of one-line statement of the Riesz Representation Theorem. I could also be cute and talk about how sexy Navier-Stokes is. Instead, how about something that underlies it all. If f ∈ C¹ where f : ℜ → ℜ^m , we can write

f(t) = ∑ c_k e<sup>ikt

Now that's sexy. But Fourier series are pretty passe, I'll admit, so I'll also throw in the geodesic equation</sup>

d²x_k/dt² + ∑_ij Γ^k_ij dx_i/dt dx_j/dt = 0

Wow, not exactly super pretty. I guess I'll just do that LaTeX thing in the future.

Anyway, that's just about it. For a fun fact about myself I'll throw in that I'm learning guitar now. For even more exciting detail, I'll confess that my inspiration is an unyielding desire to play early 90's britpop such as, e.g., Oasis. No, I'm not kidding.

Expect more fun to follow. Cheers.