[MOSAIC-news] M-CAST on Friday (finite differences as derivatives)
Nicholas Horton
nhorton at smith.edu
Thu Aug 12 07:57:33 CDT 2010
Our first M-CAST is Friday! M-CASTS are short (20 mins) presentations/conversations held every second Friday around mid-day. They are a way for instructors to share ideas and to form collaborations to test and refine those ideas in teaching the MOSAIC topics: Modeling, Statistics, Computation, and Calculus.
August 13: Daniel Kaplan, Finite-Differences as Derivatives
Time: 1:00 CDT (2:00 Eastern, 11:00 Pacific)
Abstract: Calculus students encounter differentiation as a set of rules for symbolic manipulation, x^2 => 2 x or sin => cos and so on. I'll show a computer operator for differentiation that can be written from scratch in about 30 seconds in languages such as Matlab, Mathematica, R, etc. It implements a finite-difference version of the derivative, taking a function as an input and returning a function as an output. What's the point? Why use finite differences rather than the real derivative?
• The computer notation emphasizes that differentiation is an operation on a function and produces
another "derived" function.
• The link between derivatives and slopes is explicit, rather than implicit as in the symbolic transformation rules.
• Students can investigate the consequences of NOT taking a limit, which leads naturally to the idea of examining
how good an approximation is.
• Students can explore higher-order derivatives from the beginning, without having to master symbolic manipulation first.
Instructions for tuning in are at
http://www.mosaic-web.org/MCAST/instructions.html
The schedule for the next couple of months is at:
http://www.mosaic-web.org/MCAST/mcast-schedule.html
Nicholas Horton
Department of Mathematics and Statistics, Smith College
Clark Science Center, Northampton, MA 01063-0001
http://www.math.smith.edu/~nhorton
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