Hey mathy people

[cnoocy]

What do you consider the key facts and applications that should appear in a short introduction to differential calculus?

Comments

[jordanwillow.livejournal.com]

I recommend, "What the hell is differential calculus?"

*helps*

[cnoocy]

That's definitely on the list!

[colorwheel.livejournal.com]

well, it needs to have yaks

[cnoocy]

That's more helpful than you might think.

[lorelei-sakai.livejournal.com]

How short? Are you talking elevator pitch?

I'd probably start with what a derivative is, and what an integral is, and what kinds of applications there are. The actual calculations can all be looked up or done by computer, so that's hardly important any more.

[cnoocy]

Um, 3 minutes in musical form, so not quite elevator pitch. What applications can you think of specifically on the derivative side of the fence?

[thedan.livejournal.com]

Mainly the concept that derivative equals rate of change. The example of taking average velocity over a minute, half a minute, a tenth of a minute, et cetera, is a little cliche, but I think it's the best way to give people a sense of what instantaneous velocity (and thus the derivative) means.

Depending on how short you're talking about, I think it's good to show a derivative calculation using the definition (of, say, 5x^2+3x) and then explain the power rule; that conveys the idea that calculus takes these complex calculations and compresses them into quick conversions.

[cnoocy]

Great. Thank you!

[530nm330hz.livejournal.com]

I think the best example I've heard recently was Barney Frank on the Daily Show: "Things are still getting worse, but they're getting worse slower."

[cnoocy]

Nice.

[mrmorse.livejournal.com]

This is a good example of the way in which differential calculus shows up all the time in economics. The budget deficit is the derivative of the national debt. The change in employment is the derivative of the unemployment rate. Barney Frank is talking about the second derivative in that quote.

[cnoocy]

That's very useful. Thanks!

[probably-lost.livejournal.com]

I'm trying to remember who at one point said of inflation, "the rate of increase of the rate of increase is slowing" (a statement about the third derivative!). I'll check in my calc book tomorrow (right now it's in my office and I'm not).

[kamamamama.livejournal.com]

How things that depend on each other change together.

[cnoocy]

Thanks. That's useful.