ВОЗМОЖНОСТИ ИСПОЛЬЗОВАНИЯ МЕЖПРЕДМЕТНЫХ СВЯЗЕЙ МАТЕМАТИЧЕСКОГО АНАЛИЗА И АНАЛИТИЧЕСКОЙ ГЕОМЕТРИИ НА ЗАНЯТИЯХ ПО МАТЕМАТИКЕ (ДЛЯ СТУДЕНТОВ МАТЕМАТИЧЕСКИХ СПЕЦИАЛЬНОСТЕЙ СРЕДНЕГО ПРОФЕССИОНАЛЬНОГО ОБРАЗОВАНИЯ)

Abstract

Motivation of students of mathematical specialties to study various sections of higher mathematics, in particular, mathematical analysis, has not increased in recent years. This undoubtedly leads to a gradual decrease in the level of mathematical training of students. The purpose of the article is to consider the possibilities of using interdisciplinary connections of mathematical analysis and analytical geometry in the educational process for students of mathematical specialties of the Institute of Secondary professional eduation. The article discusses the methods: 1) the implementation of interdisciplinary connections and 2) mathematical modeling. We believe that these methods will help to increase the level of motivation to study mathematical analysis among students. In particular, we consider the problems of calculating integrals using higher-order curves: ellipses, astroids, cardioids. In this regard, we use the following concepts in mathematical models from analytical geometry: Cartesian coordinate system, polar coordinate system, types of higher-order curves, their analytical expressions and images. Based on these facts, applications of certain integrals in geometric and physical problems can be carried out in the following sequence: a) first of all, students get acquainted with the curve, its analytical representation in the Cartesian and (or) polar coordinate system, its graph is constructed; b) historical information about this curve is given; c) specific tasks are proposed in which it is possible to trace the intersubject connections of analytical geometry and mathematical analysis. Main results of the work: 1) identification of intersubject connections of analytical geometry and mathematical analysis; 2) development of a methodology for the application of certain integrals in problems using higher-order curves. The theoretical significance of the study is to identify the possibilities of using intersubject connections of analytical geometry and mathematical analysis. The practical significance lies in the fact that the proposed methodology helps to increase the level of motivation of students to study mathematical analysis.