Assignment: Real Life Derivatives

Now that we have explored the meaning of the derivative of a function, let's think about some things in our worlds that can be modeled using rates of change. My example is my 1969 Volkswagen Westfalia. It is obviously old and, because I live at the beach, it has to endure the harsh elements. So, what does this have to do with functions, you ask. Well, I am constantly worrying about rust. My function is the amount of rust on my VW as a function of time, R(t). As much as I wish it were not the case, I think this is probably an increasing function. The more rust there is, the more there is going to be. Perhaps a never ending battle with the elements. Oh to own a garage.

What is the meaning of the derivative of my rust function? Liebniz would consider dR/dt...the change in the amount of rust with respect to time. In other words, the amount of rust that is added at any given moment. Argh, continuous function? Does that mean my beloved Math-Mobile is rusting away as I write this? Maybe I should get out of here and start sanding and grinding. Ah but back to the Calculus...

In this blog, I want you to consider some function in your world and discuss the meaning of the derivative of your function.

Assignment: Mastery

As we have discussed in class, our goal this year is to master the Calculus. What does this mean? When thinking of mastery, several things come to mind. One is the London Taxi Drivers' Test. Can you imagine having to take a rider anywhere in London, a city designed and built long before the advent of the automobile, based entirely on being given an address?

Another example comes from the recently released DVD of the poet laureate of the great state of New Jersey, Bruce Springsteen as he describes writing the lyrics to "The Rising." Mr. Springsteen says, "These are the songs that you wait for. Did I think of any of this prior to writing the song? Nope. But I felt all of it when I was writing the song. Over thirty years you internalize your craft and the mechanics of story telling; it becomes like a second language. You speak without thinking. It's like a second skin that you feel with. So you pray to the gods of creativity and aliveness that you remain awake and alert and in command of your senses so that when the moments arrive you are ready."

Finally, one of my favorites comes from the opening scene of the movie "Caddyshack" in which Chevy Chase plays Ty Webb:
Ty: "I like you Benny."
Danny: "That's Danny, sir."
Ty: "Danny...Let me give you a little advice. There's a force in the universe that makes things happen and all you have to do is get in touch with it. Stop thinking, let things happen, and be the ball. (Covers eyes with blindfold.) Danny, where's the wedge?"
Danny: "It's right here, sir."
Ty: "Thank you Danny. Find your center, hear nothing, feel nothing." (Hits ball over water trap and it lands within 2 feet of the hole.)
Danny: "That was incredible, sir"
Ty: "You try it. Just relax, find your center, picture the shot, Danny. Picture it. Turn off all the sound. Just let it happen. Be the ball, Danny. You're not being the ball, Danny."
Danny: "Well, it's kind of difficult with you talking like that."
Ty: "OK. I'm not talking. I've stopped talking. I'm not talking now. Be the ball. (Danny hits ball and it lands in the water.)
Danny: "Where'd it go?"
Ty: "Right in the lumber yard."

So as we embark upon our journey to attempt to master the Calculus, I want you to reflect on things in your life that you have already truly mastered. What do you do in your life where you act without thinking, where you are the ball, what is your second skin?