infojournalИнформатика и образованиеInformatics and education0234-04532658-7769Publishing House Education and Informatics10.32517/0234-0453-2022-37-1-79-86infojournal-804Research ArticleЗАРУБЕЖНЫЙ ОПЫТFOREIGN EXPERIENCEВычислительный взгляд на обучение производнымA computational point of view on teaching derivativeshttps://orcid.org/0000-0003-1072-9578МацциаФ.MazziaF.

Мацциа Франческа - профессор департамента информатики.

Бари

Francesca Mazzia - Full Professor of Numerical Analysis at the Department of Information Technology.

Bari

francesca.mazzia@uniba.itУниверситет имени Альдо Моро в БариИталияUniversity of Bari Aldo MoroItaly2022100620223717986Copyright © Мацциа Ф., 20222022Мацциа Ф.Mazzia F.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://info.infojournal.ru/jour/article/view/804

Тесная связь между математикой и информатикой подчеркивает важную роль научных вычислений во многих приложениях. К сожалению, математика традиционно преподается без изучения возможных связей между решением абстрактных задач и использованием алгоритмов, которые можно реализовать на компьютере. Поскольку математическая теория и вычислительная практика преподаются отдельно друг от друга, многие студенты не понимают полезности математики. В этой статье мы кратко объясняем, как на типичной лекции о получении производных в дифференциальном исчислении могут быть использованы примеры, реализованные на языках высокого уровня, таких как MATLAB, Python или R. Такие примеры могут помочь студентам лучше понять теоретические концепции и пределы арифметики с плавающей запятой конечной точности. Мы утверждаем, что, хотя исторические открытия Лейбница и Ньютона являются хорошей отправной точкой для введения методов аппроксимации конечных разностей, это не исключает новых подходов к численному вычислению производных с использованием бесконечной компьютерной арифметики.

The strong connection between mathematics and informatics highlights the important role of scientific computing in many applications. Unfortunately, mathematics is traditionally taught without investigating possible connections between abstract problem solving and the use of algorithms capable of being implemented on a computer. Since mathematical theory and computing practice are taught separately, many students fail to appreciate the utility of mathematics. In this paper, we briefly explain how a typical lecture on obtaining derivatives in differential calculus can benefit from examples implemented in high-level languages like MATLAB, Python or R. Such examples can help to guide the students to a better understanding of the theoretical concepts and limits of finite precision floating-point arithmetic. We argue that, while the historical findings of Leibniz and Newton are good starting points for introducing finite difference approximation methods, this does not preclude new approaches to numerically computing derivatives using Infinite Computer Arithmetic.

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The authors declare that there are no conflicts of interest present.