DIFFERENTIAL EQUATIONS IN THE PROFESSIONAL TRAINING OF MATHEMATICS TEACHER
The paper presents the results of research on the study of the course of ordinary differential equations and partial differential equations in the context of the competency approach to training future math teachers. As is known, models of real processes can be described in the language of mathematics, including by means of ordinary differential equations and partial differential equations. Ability to create such mathematical models and work with them is an integral part of the human culture. Thereby it is necessary to search for new approaches to the training of maths teachers, aimed at the formation of ideas about the role of models and modeling. In this connection the course of differential equations is essential means in attracting students to research work and for the formation of professional competence of the future teacher of mathematics. The course of differential equations plays a fundamental role in the professional training of mathematics teacher in terms of understanding the gist of the application and the practical orientation of teaching mathematics, mastery of the method of mathematical modeling. The course of differential equations and its methods give another tool for knowledge of the world, which allows to create a scientific understanding of the real physical space. The results presented in the paper allow us to conclude, that the involvement of students in research work in the framework of the course of differential equations not only promotes the overall development and professional training of the future teacher of mathematics, but also getting completely new results are important in the modern theory of differential equations and theoretical physics.