Using the Mathematica Computer System on Tylor Derivatives

Author Name(s): Anton N. Karamyshev, Zhanna I. Zaytseva, Natalia I. Gubochkina
Author Email: antonkar2005@yandex.ru

Abstract

The ability to find a derivative and use it in different fields plays a large role in the practical activities of students, both in technical specialties, and in economic, and humanitarian ones. The concept of the derivative is one of those mathematical concepts that are intersubjective in nature and are actively used in economic, chemical, physical, and other branches of science and their applications. The study of material on this topic is of great importance since it shows the possibilities of using elements of differential calculus in the description and study of processes, phenomena of the real world. In the school course of algebra and the beginnings of analysis, the concept of a first-order derivative is introduced and the rules of differentiation are derived, in the same place, it is shown in the example of the function || xy  that it does not have a derivative at zero. In the course of higher mathematics, the concept of derivative expands; the derivative of the nth order is understood to mean a function that is the first-order derivative of the derivative of the (n-1) the order. Moreover, there are functions that are continuous at each point of the set of real numbers, but at no point have a derivative. In this regard, the article examines the possibility of applying tayloresque derivative in mathematical education secondary schools in solving academic and applied tasks, and suggested ways of using the computer mathematics system Mathematica as the means for performing computation in the process of solving training tasks in the classroom and to create demonstration and simulation software tools. So, for example, under the topic “the Maclaurin Series”, we propose to use tayloresque derivatives and demonstration and simulation software tool created in computer mathematical environment Mathematica, which is based on specific software procedures of the programming language WolframLanguage.

Introduction

In recent years, there has been a noticeable decline in interest in mathematics from a certain part of pupils and students, and society as a whole, when mathematics is perceived not as an object of professional activity, but as an unnecessary science that will not be useful in future professional activities. Students do not want to spend time and effort to study such a complex, but interesting and exciting subject as mathematics. Therefore, you have to observe that students do not try to delve into the educational process, but increasingly use the Internet to solve their tasks. On the one hand, this has a positive aspect, and on the other, and it is more common, it comes down to profanity, which is called “three clicks”, that is, copied – pasted. Such an attitude to mathematics can lead to a loss of computational skills, which is undesirable since it is important for students of engineering fields to solve a mathematical problem to get an answer in the form of an exact or approximate numerical equivalent. Now the teacher, in addition to transferring knowledge, should pay great importance to enhancing the cognitive activity of students, organizing their independent work. In other words, it is necessary to introduce such methods and technologies that are not yet on the Internet and which encourage the student to actively study and develop the ability to independently solve complex mathematical problems.

Conclusion

The use of the Taylor derivative function of one variable and the Mathematica computer mathematical system in teaching allows you to intensify the educational process, reducing time spent on laborious but completely routine calculations, increasing the level of visibility and the level of information, involving students in the research process, instilling a taste for mathematical experiments. Informatization of the process of teaching mathematics enriches it with new means

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