I ran out of review problems in Anton's book, at least those concerning finding the equations for tangents at any point on a function's graph. So I went back to my collection of calculus books and retrieved Allyn Washington's "Basic Technical Mathematics with Calculus," which I described in this earlier entry. (The Electron reserves the right to be self-referential.) This is the Fourth Edition, dated 1985, and one of my Friendly Scientists actually worked as a co-writer on a later edition. I have more recent calculus books, but they demand the use of complicated, expensive calculator equipment which I don't have. I have a 15-dollar calculator which has been sufficient for anything I've done so far. My Macintosh has a graphing program which I sometimes use to check my work. I prefer to use the books which expected the student to work things out with pencil and paper.

And there in the instructions for finding equations of tangent lines was the Capital Delta, the Greek letter which is one of the unmistakable signatures of Calculus. I used to be a classicist, which like "physicist" is one of those all-encompassing vocations which takes up your whole life. In my Greek and Latin days, I had plenty of Deltas: Dionysus, Demeter, Democritus, Diomedes, Demosthenes. But this is Delta from a different discipline. The book explains:

"…The symbol (Delta) used here has no meaning by itself. The name increment is given to the difference of the coordinates of two points, and therefore (Delta)x and (Delta)y are the increments in x and y, respectively."

As the virtual Professor explained in his first DVD calculus lecture, this is all about change and motion. I am dealing with intervals and increments rather than single quantities, and processes rather than single operations. It's Delta for Difference, D for Diligent, Daring, and Dynamic.

Posted at 2:52 am | link