INTEGRATED APPROACH TO DEFINITION OF DERIVATIVE OF FUNCTIONS, WHICH IS DEFINED ON CONTINUOUS AND DISCRETE SETS - Lukashova, Tatyana; Strakh, Oleksandr (Physical and Mathematical Education, 2021)
The acquisition by a student of complex knowledge by studying generalizing theories and methods, the basic fundamental concepts are defined through which, is an important element in his training as a future specialist, in particular in the field of mathematics. Today there are a number of such theories, and their using is singled out even as methods of independent scientific directions. Applying elements of generalization and comparison of objects of study of different mathematical disciplines in the educational process, we also significantly contribute to the construction of interdisciplinary connections, which in turn have a positive impact on the comprehensive development of the future specialist and the realization of his potential in scientific and professional activities.Formulation of the problem. Analysis of the main provisions of differential and difference calculus leads to the conclusion that there are significant similarities between the properties of the derivative and the difference operator, which are based characteristics of functions that are defined on continuous and discrete sets, respectively. It turns out that this similarity is not accidental, and these concepts are partial cases of the concept of delta derivative of function.Materials and methods. The authors used the following research methods: systematic analysis of scientific, educational and methodological literature; comparison and synthesis of theoretical positions; monitoring the course of the pedagogical process; generalization of own pedagogical experience and experience of colleagues from other institutions of higher education. In addition, some general mathematical and special methods of differential and difference calculus and time scale theory were used.Results. This article considers a general approach to the study of two fundamental mathematical concepts - the concept of derivative and difference operator, as well as ways to use this approach to establish connections between different mathematical theories in order to form a holistic view of mathematical objects, their properties and application.Conclusions. Establishing connections between models and research methods used in the study of various mathematical disciplines included in the training program for future specialists in mathematics, allows students to form a holistic view of mathematical objects, algorithms and theories, and as a consequence, makes them knowledge is systematic and practically more significant. This contributes to the intellectual development of students, the formation of their systematic mathematical knowledge, increasing the level of mathematical literacy and interest in mathematics.
Keywords: derivative; difference operator; delta derivative; differential calculus; continuous set; discrete set