Applications of a Derivative Function of One Variable

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

Abstract

The relevance of the topic of this article is derived from the education informatization process – the process of providing the education sector with the methodology and practice of the development and optimal use of modern computer technologies, and therefore – with the necessary changes in the content of education, its structure and the introduction of new computer technologies in the educational process. The purpose of this article is the methodology of using information technology in the educational process of teaching mathematics by creating and using new forms of software pedagogical products using advanced computer technology. The leading method for studying this problem is the methodological analysis and subsequent synthesis methods, which allows identifying the necessary ways and methods for creating a pedagogical program product by analyzing the didactic content of the section “Differential calculation of the function of one variable” of the university course in higher mathematics, as well as the instrumental capabilities of the Mathematica mathematical computer environment. The article describes the main aspects of the work of a mathematics teacher, who is not a specialist in programming, in compiling and using a simulator in the educational process on the topic “Application of the derivative function of one variable” using the Mathematica computer mathematical system. Article materials may be useful for the teachers of mathematical disciplines of higher educational institutions. The simulator on the topic “Application of the derivative function of one variable”, which was created and intended for use in the Mathematica computer mathematical system, can serve as an example of the development of similar pedagogical software products.

Introduction

The application of differential calculation, in particular, the derivative function of one variable, is a powerful tool for solving applied tasks, as we know. The representatives of various specialties have to work with this type of tasks: process engineers organize production so that the enterprise can produce as many products as possible; designers are developing new devices for spacecraft with an optimal reduction in their mass; economists are trying to build more profitable transport links for the enterprises between the sources of raw materials and the production facilities, etc. Here is a list of some practical problems that can be solved using the derivative: 1. It is necessary to make an open box of the greatest volume from a rectangular tin sheet measuring 25×40 cm. You need to cut square corners for this purpose. Depending on the cut square size, the boxes with different volumes are obtained. Therefore, it is important to calculate the side length of the cut squares so that the entire box has the largest volume. It is used the ability to find the extremum of a function of one variable to solve this task. [3,4] 2. The charge flowing through the conductor varies according to the law ) 102sin(  tq .Find the current strength at time t = 5 sec. It is used the ability to find the value of the first derivative at a point to solve this task. 3. An electric heater consumes power from a current source, whose EDS is 3 V and internal resistance is 2 Ohms. What resistance should the device have to release maximum power? It is used the ability to find the extremum of a function of one variable to solve this task.

Conclusion

The ability to quickly receive timely correction of training activities in the process of working with the simulator on the topic “Application of the derivative function of one variable” created in the Mathematica computer mathematical system stimulates students to develop their skills on this topic. This leads to an acceleration of the pace of learning, frees up time, therefore, intensifies the learning process.

 

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