4:00 pm Friday, March 9, 2012
Sophex: Calculus on Fractals by Dennis Kriventsov (UT Austin) in RLM 10.176
On the real line, there are two derivatives each calculus student studies: a first-order one which quantifies rate of change and a second-order one which describes deviation from flatness. These are easily generalized to several dimensions and smooth manifolds, but retain the same orders. Instead, we'll consider the Sierpinski Gasket (a fractal of dimension log3/log2), where the second derivative can be defined analogously to the line, but ends up having a different order. We'll also look at analogues of lines, polynomials, first derivatives, and energy. No prerequisites needed! Submitted by
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