Tuesday, July 16, 2013

Tuesday: Chain rule

It turns out that given f(x,y), if y = y(x), then df/dx != ∂f/∂x.  I have a solution that looks like it should be correct, but it doesn't seem to work quite right.  This suggests I probably should look at numerical derivatives, and compare those with the analytic ones.

I was able to prove that a four term Fourier expansion of the function is effectively equivalent to the five term polynomial + special function expansion I've been using.  Always a nice thing to see.  The Fourier expansion is probably faster, as I suspect sine and cosine are probably well optimized (and are apparently part of the processor instruction set).

All this math has made me hungry.  For pizza.  That looks like a frozen pizza, too.  I could get a frozen pizza tomorrow, and eat it for dinner.  Not like the whole thing.  I've not done enough math for that much pizza.  Just a slice or two, with something healthy to make it a proper meal.  I have a big tub of grapes that would probably go well.  Maybe get some lettuce and do a salad?  Can you put grapes in a salad?




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