...Prove Their Worth...

"Problems worthy of attack
prove their worth
by hitting back." - Piet Hein

A kind of running diary and rambling pieces on my struggles with assorted books, classes, and other things, as they happen. You must be pretty bored to be reading this...

Friday, June 07, 2002

I'm just about ready to beat my head on the nearest wall. It has to do with that Schwarzian derivative I mentioned earlier. Here's the problem. I'm supposed to show that there's a certain 'chain rule' for it. That is, assign w = f(z), f being analytic. The question then becomes, what is the Schwarzian derivative of g(w), where g is another analytic function. Now, in Needham, the rule is given:

{g(w), z} = (f'(z))^2 * {g(w), w} + {f(z), z}

The problem is that I can't for the life of me show that to be true. I just get lost in an endless swamp of algebra and calculus, and never really come out. Normally, I'd just blame myself for my ineptness. There is, however, a small chance that the above equation actually isn't quite right - there might be a typo. I've found a couple of places that give something that looks a lot like it, but with one (1) extra parenthesis. So those sources definitely have typos. But the question is, did they want to have a couple of extra parentheses, or none? I'm confused. What's even worse is that I can show something almost, but not quite, like the given formula. Aarrrrrrgh.


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