APPLICATION OF THE THEORY OF DIFFERENTIAL EQUATIONS TO SOLVING MATHEMATICAL PROBLEMS

Abstract

Introduction. The courses of mathematical analysis and differential equations are
one of the main basic courses of the mathematical cycle of disciplines, which are studied by students
of mathematical, physical, technical, IT specialties of higher education institutions, etc. As our studies
have shown, acquisition and, most importantly, the application of a set of a large number of different
mathematical facts and concepts in the process of solving problems often lead to the appearance of
difficulties in achievers. As shown by our studies, assimilation and, most importantly, the application
of a set of a large number of different mathematical facts and concepts in the process of solving
problems often lead to the appearance of difficulties in learners. Therefore, the method of their study
should be built as specific for this category of students.
The purpose of the article is to consider the peculiarities of the application of the theory of
differential equations and methods of finding different types of integrals for solving problems of
geometric and mechanical content and to take them into account during the training of students in the
fields of 01 Education/ Pedagogy, in particular 014 Secondary Education, 11 Mathematics and
Statistics, 10 Natural Sciences sciences, 12 Information technologies, formulate appropriate
recommendations.
Originality. in the article, we indicated the vectors that should be used with students to
consolidate and reproduce the methods of solving differential equations when solving problems in
geometry and physics. Exercises have been developed in accordance with four levels of the formation
of a mathematical concept: 1) the student's scattered idea of a phenomenon, subject, etc.; 2) the
student can distinguish one concept or phenomenon from another, name the features of the concept,
but does not distinguish essential properties from non-essential ones; 3) the student learns essential
and non-essential properties, but cannot generalize concepts; 4) the student can generalize concepts,
freely operates with them.

Conclusion. We see further research in the development of a system of preparatory
differential problems to prepare for solving geometric and physical problems using differential
equations.