some people have a little analyst in them, some don't (also: fanboy wisdom)

today in calculus we discussed multivarιate limits. admittedly, when i studied calculus, i liked it. when i teach it now, i still find it quite fun ..

.. or rather, i enjoy writing the lecture.

like the cut of a good sports jacket, it's rare but enjoyable to employ the squeeze theorem in such casual settings.

admittedly, it sates that little analyst in me. (-;

lecturing this lesson to an undergraduate american [1] audience is something else, though.

this topic, i think, is just as unnerving to a student as when (s)he realises that there's no formulaic way [2] to determine whether an infιnite series converges or diverges.

it's easy to tell this. every time i give this lecture, several students ask, in various forms and in various levels of sophistication,

"are you sure there's not a cookie-cutter way to do these problems?"

i guess not everyone has a little analyst in them. q-:

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on a slightly related note: in the same lecture i gave an example of a function which diverges at (0,0) but whose directional limits, along lines, always gave the value 0.

having checked lines, i paused and then said,

"there's a reason for why this isn't working.
you see, we're thinking too much like superman;
we should think like batman!"

heads shot up, wholly surprised. i continued:

"ok: imagine (0,0) as lex luthor. what does superman do? he flies straight at him, mustering up as much momentum as possible. does he make it? no! lex luthor has a kryptonite shield, and supes just crumples and falls, just as he reaches lex!"

a few students now begin to laugh.

"but what would batman do? he would survey the situation, and when he knows the right path, he'll swoop in. lex won't see him -- who sees batman coming, anyway? -- and we'll be able to detect a nonzero limit."

"so let's say that batman swings in a parabolic arc .. that makes sense, with the jumpline and all .."

somehow i get the feeling: if my students learn any one opinion from me, it's that batman is always better than superman.

[1] this is not a knock on americans. having never given lectures abroad, i just don't know whether the same unease persists in other countries. thoughts?

[2] odds are that someone out there has written out a complete, complicated flowchart on how to solve any elementary problem of that sort. i don't doubt it. then again, similar charts probably exist on how to decide what to have for lunch, when in a shopping mall.