Many students of calculus are not aware that the calculus they have learned is a special case (integer order) of fractional calculus. Fractional calculus is the study of arbitrary order derivatives and integrals and their applications. The article begins by stating a naive question from a student in a paper by Larson (1974) and establishes, for polynomials and exponential functions, that they can be deformed into their derivative using the μ-th order fractional derivatives for 0<μ<1. Through the power of Excel we illustrate the continuous deformations dynamically through conditional formatting. Some applications are discussed and a connection made to mathematics education.
2009 HERDC submission. FoR code: 0103
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Miller, David A. and Sugden, Stephen J.
Insight into the Fractional Calculus via a Spreadsheet,
Spreadsheets in Education (eJSiE):
2, Article 4.
Available at: http://epublications.bond.edu.au/ejsie/vol3/iss2/4