My weblog ELECTRON BLUE, which concentrated on science and mathematics, ran from 2004-2008. It is no longer being updated. My current blog, which is more art-related, is here.
Fri, 06 Oct, 2006
Calculus Review Panic, episode 2
I have now spent more than four months on learning about limits and instantaneous velocities. Yet when I returned to the sets of problems that I had already done (in August) I found that I had forgotten how to do them. This was dismaying, but not unfamiliar. I doubt whether I could solve any of the trigonometric identity problems I solved back in 2004, let alone the logarithm problems I struggled over later that year. And if I were called upon to do one of those sliding block problems in first year physics, I couldn't work it right away. I'd have to look back at my notes and the relevant text in the book before I could solve it.
As a solitary learner, I don't know whether this is typical or whether I am just, well, dim. I found pencilled notes in my calculus textbook from a couple of months ago, that made no sense to me now. In fact, one of them was completely wrong, a result of mistaking one problem for another, and I had to erase it. I patiently went over the instructional chapter again on finding limits for various kinds of functions. "Divide the numerator and denominator by the highest power of x that occurs," says author Anton helpfully. Then set x to zero, or find out what would make the various denominators go to that forbidden zero. Somewhere in that process, a limit emerges.
These are techniques that are still new to me. I guess I will have to do these calculations many, many times before they become familiar. They are mechanical and remind me of clockwork, or a mathematical crank that I can turn as long as I have the right handle or key. It has a kind of Enlightenment early-industrial feel to it, just like the seventeenth century era in which calculus was born. I will have to turn a lot of wheels before I can make this engine work.
Posted at 3:01 am | link