INTERDISCIPLINARY CONNECTIONS IN THE STUDY OF SOME TOPICS OF DISCRETE MATHEMATICS AND DIFFERENTIAL EQUATIONS

Abstract

Abstract. One of the important tasks in the training of future specialists in the branch of mathematics is the expansion and deepening of mathematical knowledge in order to apply them comprehensively in practice, in future scientific and professional activities. One way to implement this task is to use interdisciplinary connections that involve the transfer of research methods and research models from one scientific discipline to another.

Formulation of the problem. This article considers the possibility of implementing interdisciplinary connections of discrete mathematics with differential equations on the example of studying the topics «Linear recurrence relations with constant coefficients» and «Linear differential equations with constant coefficients».

Materials and methods. The authors used the following research methods: systematic analysis of scientific, educational and methodological literature; comparison and synthesis of theoretical positions disclosed in scientific and educational literature; generalization of own pedagogical experience and experience of colleagues from other institutions of higher education. In addition, some general mathematical and special methods of the theory of differential equations, discrete mathematics and difference calculus were used.

Results. One of the ways to solve linear homogeneous recurrence relations with constant coefficients is to compile a characteristic equation and write the general solution of a given relation depending on the values of the found characteristic roots. A similar algorithm is used to find the general solution of linear homogeneous differential equations with constant coefficients. The article establishes a connection between the solutions of recurrence relations and differential equations, the characteristic equation of which has the same form.

Conclusions. Establishing connections between models and research methods used in the study of various mathematical disciplines included in the training program for future mathematicians, allows students to form a holistic view of mathematical objects, algorithms and theories, and as a consequence, makes their knowledge is systematic and practically more meaningful. This contributes to the intellectual development of students, the formation of their systematic mathematical knowledge; increase the level of mathematical literacy and interest in studying the discipline.