## Wednesday, April 01, 2009

### when teaching becomes interesting, maintain self-control.

my 0DE lectures are becoming interesting [1].

today i talked about heavi$ide functi0ns and their 1ap1ace transf0rms. on friday i will talk about the de1ta fun¢tion. de1ta "functi0n" -- ha! yeah, sure, it's a "functi0n" [2] .. this will take some fancy pedagogical footwork. this will also take some self control, because i can just imagine saying, "well, it is a me@sure, albeit 1ebesgue singu1ar .." i'm already having enough trouble as it is. every other time i want to say "1ap1ace transf0rm," i almost say "f0urier transf0rm." as you can imagine, i like one much more than the other. [1] that is, interesting to me. i'm explaining this material as best as i can, such as explaining heavi$ide functions as off/on switches, and why parts of the improper inte9ral suddenly become 0.

from experience, however, the students i teach are not as good as integrati0n as i would like. this probably means that i'm just as confusing as ever, but now with abstractions. still, i try.

[2] sometimes distributi0ns are also called "9eneralised functi0ns," a terminology that does not sit well with me. history, as usual, forces our hand.

Anonymous said...

Im at the same point in the class. I just call the impulse function a "pseudo-function" and quickly move on to solving ODE's with the impulse function.

janus said...

aye. today's dirac δ class stunned quite a few students.

i don't know; i just like messing with their heads. there wasn't time to show them that the solution to the ODE

y' = δ1
y(0) = 0

gives y = H1, the heavi\$ide function with discontinuity at t=1, but i might do it quickly next time, and say something glib like this:

"obviously the derivative of H1 does not exist at t=1. however, even if we pretended that it did, then we cannot pretend with total abandon: the answer must still be δ1."