I Take Back All The Freakouts

Yea ok, I take back all my worries about the calculus final. It was trivial.

There is one problem I'm worried about - somehow I managed to show that the flux of the Coulombic vector field (r/r^3, where r = ||r||) over a unit sphere is always 4pi if the sphere is centered on the x-axis (not just the origin). Intuitively, this doesn't make sense, but we'll see what happens when marks come out. Other than that, stupid final.

As an example, here's a toy problem for you: prove the generalized integration by parts formula

\iiint_D f(\nabla\cdot\mathbf{G}) dV = \iint_C (f\mathbf{G}) \cdot \hat{n} dS - \iiint_D \mathbf{G} \cdot \nabla f \, dV

where the boundary of D (open in R^3) is C (a single, orientable closed surface), n-hat points outward, and we have the usual "nice" conditions (i.e. f, G are C¹ over D and C; f is a scalar field and G is a vector field).

(If you want I can give you the slightly harder problem that follows this one, but that one's actually pretty easy too, just longer.)

Of course, an easy final is a wonderful thing, given that I ran more calculations instead of studied for the 6 hours before the final. Naturally, my calculations decide to fly in the face of known facts. I will need to consult my supervisor and The PI on Monday. Again. Sigh.

There's the work report too. I really don't know what to say - the data will be (kind of) all there soon, but conclusion? what conclusion? ("More work needs to be done...")

On an unrelated note - shoutout to roommates who are leaving: aww, y'all are leaving...thanks for being awesome all term!