One of the key disciplines studied in high school is algebra and the beginning of analysis. This course in grades 10-11 is taught at three possible levels: specialized training, in-depth study, basic course. In addition, there are schools with integrated lectures on the basics of higher mathematics and olympiad training courses.
However, be that as it may, any of the above profiles implies studying the “Mathematical Analysis” section, which is fundamental for those students who wish to continue their studies at a higher or secondary vocational educational institution in engineering, medical, and economic fields. In addition, mathematical analysis is part of the exam, and therefore knowledge of this section is one of the important components for passing the math exam.
The course begins with the components included in the Introduction to Mathematical Analysis: derived functions and its properties. Here, students learn about the concept of a derivative, learn to take basic derivatives according to basic formulas and rules. It is worth noting that before the introduction of the concept of derivatives, some teaching materials imply an initial familiarization of students with the concept of the limit in the framework of the course "Mathematical Analysis". The limits are studied as a basic element, without going into the details of entering this concept (which will be given in the course of higher mathematics at a university or college). When studying the relationship between a derivative and a function, it is very important to pay attention to the relationship of graphs, to learn to understand the relationship of these concepts, because this will be necessary for the successful development of subsequent material.
Mathematical analysis in the 10th grade stops on the concepts of the derivative, and then a course of probability theory and mathematical statistics follows . A return to the limits and derivatives occurs in the first half of the 11th grade, when new concepts are introduced - the primitive function, the 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 and measurement materials of the exam, however, 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 at school, it is worth noting that the authors of modern courses in algebra and the beginning of analysis at the senior level very well located it. Indeed, the beginning of the study of algebra in the 10th grade is associated with the concepts of trigonometry, the repetition of basic concepts and functions. Further, the second half of the year is devoted to limits and derivatives, where 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 grade, the mechanism of the two-way relationship between the derivative and the function is considered, the concept of the non-moving integral is given, i.e. derivative for which it is impossible to write a primitive, based on modern concepts of mathematics. Students are not informed how such integrals are taken - there are special higher education courses for this, however, to formulate a general picture, 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 the majority of the time teaching algebra in grades 10-11. Therefore, it is important that students from the very beginning understand the importance of this section for mathematics and life, can operate on basic terms and formulas, and are able to put their knowledge into practice.