Duff Campbell - USMA at West Point
Multiplicative Calculus
This talk is based on a paper by Dick Stanley of UC Berkeley. He looked at "Multiplicative Calculus" based on a multiplicative rate of change rather than an additive one. Thus we define f*(a), the *-derivative of f at a, to be the limit as h approaches 0 of (f(a+h)/f(a))^(1/h). Stanley shows that f*(a) exists iff f'(a) exists, develops some specific [if f(x) = x, then f*(x) = e^(1/x)] and general [*Product Rule, *Chain Rule] rules for *-derivatives, looks at "multiplicative approximations", etc. After reading this paper last year I wrote two projects based on these ideas for my Real Analysis I students. I will discuss the content and success of these projects. Currently, my colleague Jim Rolf and I are exploring ideas based on Stanley's paper.
Audience:
Undergraduate students are encouraged to attend. Much of this talk will be accessible to students who have taken Calculus I and Calculus II.
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