## Tuesday, December 14, 2010

### idle bits (teaching).

odd. most of my students dislike spherical coordinates. it surprised me that everyone did one particular homework problem using them, though it was avoidable.

Let $\mathcal{S}$ be the part of the sphere $x^2+y^2+z^2=4$, $y \geq 0$, oriented in the direction of the positive $y$-axis. Compute $\iint_\mathcal{S} \vec{F} \cdot d\vec{S}$, where $\vec{F}$ is ..

[thinks]
[sighs]
[gives up]

.. some vector field that has nice derivatives. (i forget.)

when i wrote the solutions, i used a parametrization with coordinates $x$, $z$. out of 100+ homeworks, only 1-2 students did the problem the same way that i did it.

on a related note, i have a soft heart. since it's finals week, i'm letting my undergrad graders off and grading the last homework and quiz myself.

no good deed goes unpunished. i thought that this week would be mathematically luxurious: spend all day with research and other matters. instead, even though classes are over, i am still working on teaching things ..!