Tuesday, January 30, 2007

My Schrodinger's Cat moment

This may sound extreme, even crazy...perhaps. But just keep an open mind for a minute. You see, this morning, i experienced something of a Schrodinger's cat moment. Mercifully, it did not have to do with the life and death situation depicted here. Nevertheless, i experienced two emotional states simultaneously--a mixture of being happy and not-happy at the same time. The not-happy state came from my being forced to abandon an old but much loved calculus book, "Calculus with Analytic Geometry" by A. B. Simon. The happy state was induced by my discovery of a new, excellent alternative, Calculus by G. Strang.

The Simon had been a surprise birthday gift from a friend, back in the 80s. It served me for years as a faithful reference, coming to my rescue more than once when i needed a quick brush-up on this or that topic in a hurry. But, attached as i am to this hard-covered and heavy old tome, it has been increasingly difficult to carry it along on my frequent international travels. So i began searching for a downloadable, well-written and comprehensive textbook online. i figured that such a book, combined with the Derive software on my machine, should greatly facilitate my ongoing adventure in self-learning, without the hassle of lugging a big book around.

So, when i stumbled upon a PDF version of Calculus by Strang freely available on the MIT OCW site, what else could i do but gleefully grab the whole shebang. Granted, the quality of the PDFed Strang leaves something to be desired, but that minor blemish can immediately be dismissed as a small price to pay for the sheer clarity and elegant brevity with which Strang handles the introduction to the subject. For example, he starts Chapter 1 with "The right way to begin a calculus book is with calculus." Strang follows this with a quick introduction to the central question of calculus:
Notice that the units of measurement are different for v (velocity) and f (distance). The distance f is measured in kilometers or miles (it is easier to say miles). The velocity v is measured in km/hr or miles per hour. A unit of time enters the velocity but not the distance. Every formula to compute v from f will have f divided by time.

The central question of calculus is the relation between v and f.
....We need to know how to find the velocity from a record of the distance. (That is called differentiation, and it is the central idea of differential calculus). We also want to compute the distance from a history of the velocity. (That is integration, and it is the goal of integral calculus.) Differentiation goes from f to v; integration goes from v to f. We look first at examples in which these pairs can be computed and understood.
As i delve deeper into Strang's Calculus, it seems as if i am reading my old Simon! Both authors seem to be one of a rare kind, possessing the same ability to communicate deep truths to the uninitiated in simple, unambiguous language. As this realization of sameness deepens, i realize that, far from betraying Simon, my download of Strang actually honors both authors while enriching my library! And, just like that, my Schrodinger's Cat moment suddenly passes, and i feel myself collapse, thankfully, into a single happy state!

1 comment:

Alice C. Linsley said...

Please start posting again. I enjoy this blog.

I'd love to see you do something on the mathematics of calendars.