Marina Hohlova

The article examines the existing in academic literature approaches to the definition of "geometric vector" concept. The authors offer, reasonable from the viewpoint of physical-technical disciplines, definition of "vector value". they investigate specifics of the operations on vectors defined in physical space. The differentiation of vector values adopted in physical and technical applications is discussed.

The article explores the possibilities of continuity principle implementing in the framework of "school - university" in the construction of mathematical problems system. As an example, a set of tasks is proposed for studying the concept of "polygonal function" in the topic "Operational calculus". It is shown that the application of the continuity principle helps to develop skills necessary for this concept learning.

The paper is devoted to possibilities of comparison and analogy in the study of some branches of mathematical analysis at university. The authors examine the application of scientific methods in the study of the section "Functions of several variables". It is shown how analogy can help in understanding of basic concepts and theorems of this section.