Sunday, April 11, 2010

Derivative Love

On the Times web site, Steven Strogatz offers a nice discussion of our friend the [calculus] deriviative:
Derivatives are all around us, even if we don’t recognize them as such. For example, the slope of a ramp is a derivative. Like all derivatives, it measures a rate of change — in this case, how far you’re going up or down for every step you take. A steep ramp has a large derivative. A wheelchair-accessible ramp, with its gentle gradient, has a small derivative.

Every field has its own version of a derivative. Whether it goes by “marginal return” or “growth rate” or “velocity” or “slope,” a derivative by any other name still smells as sweet. Unfortunately, many students seem to come away from calculus with a much narrower interpretation, regarding the derivative as synonymous with the slope of a curve.

Like many, I did not appreciate calculus in my first encounters with it, but it grew on me when I was in economics graduate school. I think its possible (though difficult) to make it as an economist without being a natural at math, but, at some point, you must learn to like it.

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