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Proceedings of the 2019 Undergraduate Mathematics Day

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Manipulations of Taylor series expansions of increasing numbers of terms yield finite difference approximations of derivatives with increasing rates of convergence. In this paper, we consider central difference approximations of arbitrary order of accuracy. We derive explicit formulas for the weights of terms and explore their limits for increasing orders of accuracy.


Finite Difference formulas, first derivative




This paper was presented Saturday, Nov. 2, 2019, as part of Undergraduate Mathematics Day at the University of Dayton. Launched in 2003, Undergraduate Mathematics Day is held in odd-numbered years and alternates with the Biennial Alumni Career Seminar. The conference coincides with the annual Schraut Memorial Lecture, named Kenneth “Doc” Schraut, a mathematics faculty member from 1940 to 1978 and department chair from 1954 to 1970.

The 2019 Schraut lecturer was Tommy Ratliff, professor of mathematics at Wheaton College in Norton, Massachusetts, who presented the lecture “So How Do You Detect a Gerrymander?” His recent research hastaken up mathematical questions related to redistricting and gerrymandering, and he has been involved with the Metric Geometry and Gerrymandering Group based at Tufts University and Massachusetts of Technology.

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