by Terry Featherstone

Created on: December 24, 2011   Last Updated: December 26, 2011

No doubt about it. Many students consider calculus scary, right up there with monsters under the bed. Calculus is the Minotaur or St George's dragon. Sadly, schools have done little to undermine its almost mythological reputation, what with “derivatives” and “integrals” and those frightening numberless equations recognizable by the initial elongated “S.” There is like, what? 100 equations, that, according to most teachers, need to be memorized?

It is too bad, because calculus is really the Wizard of Oz, terrifying to behold, but quite tame behind the curtain. Did you know that most people do calculus in their heads all the time? In fact, because the numbers associated with calculus are ever-changing, moment by moment, doing calculus with numbers is a bit pointless. A mother filling the bathtub very often does not want to stand there and watch the water. She knows that the water is coming out of the faucet at a certain rate. She knows the bathtub is filling at a certain rate. Every moment the volume of water is changing. Yet, she reliably checks the tub before it overflows.

The high school quarterback and his wide receiver communicate an even more difficult calculus on the field, seemingly by telepathy. The quarterback never aims the ball at the place where the receiver is standing. That mental math is too easy, more like algebra or even arithmetic. No, he aims the ball toward the place he hopes the receiver will be. In his head, he calculates the trajectory of the ball, the amount of force necessary (oh my gosh, not physics, too!), the speed of the receiver, and every other factor. And most of the time he gets it right, and the pass is completed. The fun thing about calculus is that the numbers are ever-changing. It is like hitting a moving target, whereas algebraic numbers thoughtfully stand still.

At its core, calculus is nothing but slope. Remember humble slope, change in y over change in x. Slope is an expression of rate, such as, change in miles over change in time, most commonly called “miles per hour” or mph. The graph is a straight line, so you can pick any two points to find the slope. But what if the graph is curved? If you were to magnify each point and extend its line, every point has a different slope. That is because straight lines illustrate rates like speed (velocity), while curves illustrate rates like acceleration (getting faster and faster each moment), just like the football getting slower

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