ОБ УНИФИКАЦИИ ИЗЛОЖЕНИЯ КРАТНЫХ, КРИВОЛИНЕЙНЫХ И ПОВЕРХНОСТНЫХ ИНТЕГРАЛОВ НА ИНЖЕНЕРНЫХ НАПРАВЛЕНИЯХ БАКАЛАВРИАТОВ

Abstract

In modern world, the up-to-date trends in reforming of higher education lead to a significant reduction of classroom activities in the educational process, which extremely negatively affects the study of disciplines of the mathematical cycle due to their abstractness and often complexity of material presentation. Thus, there is a necessity to increase the efficiency of contact work and to widen the role of unsupervised work of students. This problem is especially evident in the study of the topic “Integral calculus for functions of several variables” in the engineering directions of undergraduate studies. One of the factors that contribute to increasing the efficiency of contact and unsupervised work is the unification of the educational material presentation related to this topic. In this article, we suggest a new approach to the study of multiple, curvilinear and surface integrals in the engineering directions of undergraduate studies, which include a unified parallel consideration of these integrals when using: 1) a preliminary revision of the topic “Defined integral” and the study of new material on this basis, 2) interdisciplinary connections, 3) information technologies. It is advisable to use appropriate methodical support to improve the effectiveness of this approach. As the latter, it is appropriate to use tutorials, problem books and individual tasks, posters and 3d models, interactive guidelines integrated with applications, written in high-level languages, generators of typical tasks, etc.