CONCERNING THE DEVELOPING OF AN ELECTIVE COURSE ON THE ELEMENTS OF THE THEORY OF DIFFERENTIAL EQUATIONS FOR STUDENTS OF INSTITUTIONS OF GENERAL SECONDARY EDUCATION

Abstract

Formulation of the problem. Competence on the grounds of the theory of differential equations seems to be an urgent request for modern natural-mathematical and economic higher education. At the same time, the present programs of math courses at institutions of general secondary education make no provisions for mastering even some elements of the corresponding theory. In spite of this, in fact, even students of the ninth form meet with the integration of differential equations in the courses of physics, according to mastering the properties of uniformly accelerated motion and radioactive decay; the corresponding formulas are offered to them without any proofs. Such a situation in no way favors the development of logical and critical thinking of students and contradicts the concept of introducing some elements of research into the educational process at the level of secondary education. The introduction of the elective course on the theory of differential equations for students of senior classes of institutions of general secondary education is proposed as a reasonable temporary step to solve the existing problem.

Materials and methods. The study is based on a comparative analysis of programs and textbooks on mathematics and physics for students of the 9th, 10^th, and 11^th forms of general secondary education institutions, according to their consistency in the explicit or implicit use of the concept of a differential equation and its solution. Inductive and deductive reasoning are used for it.

Results. Content of the suggested elective course for the students of 10-11 forms and methodical recommendations for its implementation in the educational process are represented.

Conclusions. Present materials do not require students to have too deep knowledge of the relevant sections of mathematical analysis, they are quite accessible for students of 10-11 grades. At the same time, their content undoubtedly will be useful both for students' awareness of the presence of deep connections between mathematics and physics, and, perhaps, from a propaedeutic point of view taking in the mind their further study on the next level of education.