Using Freeware Mathematical Software in Calculus Classes

International Conference on Mathematics and its Applications in Science and Engineering (ICMASE 2020), on-line conference. July 9-10, 2020. 10 páginas, 10 figuras.Due to the Bologna Accord, the teaching of mathematics has undergone importantchanges. Some of the most visible modifications have been the need to complementthe traditional teaching-learning process with practical, real-life cases and thepossibility to reinforce the introduction and usage of key concepts throughmathematical software.Nowadays, there exist many computational packagesdealing with mathematics, some of the best-known being Mathematica and Matlab.However, although they are very complete and powerful, they demand the use ofcommercial licences, which can be a problem for some education institutions orin the cases where students desire to use the software in an unlimited number ofdevices or to access from several of them simultaneously.In this article, we show how to apply GeoGebra and WolframAlpha to the processof teaching Calculus to first-year university students.While GeoGebra is aninteractive geometry, algebra, statistics, and calculus application available both asan online resource and a native application in Windows, macOS, and Linux systems,WolframAlpha is a computational knowledge engine developed by a subsidiaryof Wolfram Research, the company behind Mathematica. However, unlike thatproduct, WolframAlpha can be accessed by any individual as a web service free ofcharge. One of the key aspects of WolframAlpha is the possibility to use naturallanguage and Mathematica syntax for requesting computations, which allows usersto benefit from a large amount of Mathematica resources.Being able to use GeoGebra and WolframAlpha as web services withoutdownloading and installing software is another important advantage, as it avoidsthe need to have adminstrator rights to use those computational engines, whichtypically represents a problem in education centres where lab computers arelocked so students cannot inadvertently install malware that can compromise theuniversity’s network.As the best way to show a topic in mathematics is to provide examples,this contribution focuses on the main topics associated to a first-year Calculus class (limits, continuity, derivatives, curve interpolation and integrals), providingexamples with GeoGebra and WolframAlpha for the computations and concreteexamples used in actual Calculus classes.This work was supported in part by the Ministerio de Economía, Industria y Competitividad (MINECO), in part by the Agencia Estatal de Investigación (AEI), in part by the Fondo Europeo de Desarrollo Regional (FEDER, UE) under Project COPCIS, Grant TIN2017-84844-C2-1-R, and in part by the Erasmus+ program of the European Union under grant 2017-1-ES01-KA203-038491(RULES_MATH). Víctor Gayoso Martínez would like to thank CSIC Project CASP2/201850E114 for its support