The role of the course "Mathematical analysis" in the senior part of the school

One of the key disciplines studied in the senior link of secondary school is algebra and the beginnings of analysis. This course in grades 10-11 teaches at three possible levels: profile preparation, in-depth study, a basic course. In addition, there are schools with integrated lectures on the basics of higher mathematics and olympiad training courses.

However, however, any of the above profiles implies the study of the section "Mathematical Analysis", which is fundamental for those students who wish to continue their studies in engineering, technical, medical or economic fields in higher or secondary vocational schools. In addition, mathematical analysis is included in the tasks of the USE, and therefore the knowledge of this section is one of the important components for the successful passing of the exam in mathematics.

The beginning of the course begins with the components included in the "Introduction to mathematical analysis": the derived functions and its properties. Here, students learn about the concept of the derivative, learn to take the basic derivatives of the basic formulas and rules. It is worth noting that, before the introduction of the notion of derivatives, some QMSs imply the primary familiarization of students with the notion of a limit within the framework of the course "Mathematical Analysis". Limits are studied as a basic element, without going into details of the introduction of this concept (which will be given in the course of higher mathematics at the university or college). When studying the connection between a derivative and a function, it is very important to pay attention to the interrelation of graphs, to learn to understand the interrelation of these concepts, since This will be necessary for the successful mastery of the subsequent material.

Mathematical analysis in the 10th class terminates on the concepts of the derivative, and then follows the course of the theory of probability and mathematical statistics. Return to the limits and derivatives occurs in the first half of the 11th class, when new concepts are introduced - an antiderivative function, a definite and indefinite integral. To date, the material of mathematical analysis studied in the last grade of the school is not included in the control materials of the USE, but familiarization with these concepts is very important for the formation of the mathematical culture of students and their preparation for studying the course of higher mathematics in other educational institutions.

Considering the position of the course of basic mathematical analysis in school, it is worth noting that the authors of modern algebra courses and the beginning of analysis in the senior link very successfully placed it. Indeed, the beginning of the study of algebra in the 10th class is associated with the concepts of trigonometry, the repetition of basic concepts and functions. Then the second half of the year is devoted to limits and derivatives, where the previously obtained knowledge is expanded and deepened by introducing the concept of an object of "similar nature" that accompanies each function in mathematics. In the 11th class there is a consideration of the mechanism of the two-way interrelation between the derivative and the function, the notion of the non-forming integral is given, i.e. Derivative, for which it is impossible to write an antiderivative, based on modern concepts of mathematics. Students are not informed how such integrals are taken - there are special high school courses for this, however, to focus on this aspect, it is very important to focus on this aspect.

The course "Mathematical Analysis" in high school is an important and fundamental course, which, in fact, takes most of the time teaching algebra in 10-11 grades. Therefore, it is important that students from the outset understand the importance of this section for mathematics and life, could operate with basic terms and formulas, and be able to apply the knowledge gained in practice.