The development of scientific outlook of students when teaching inverse problems for differential equations

Abstract

Problem and goal. Modern achievements of the world Science of nature and the world, physical laws and laws should be disclosed at an accessible level to University students. Among the scientific methods of research of physical processes and phenomena, an important place is the method of mathematical modeling, because mathematical models have scientific and cognitive potential and versatility (see, for example, [2-4]). The use of mathematical models of inverse problems for differential equations (IPDE) allows to effectively investigate many processes and phenomena occurring in the air, earth and water environment. It is not surprising that in some Russian universities in the physical and mathematical areas of training are taught IPDE in the form of a choice of courses. The goals and objectives of such teaching are set, as a result of which students would develop creative mathematical abilities, formed fundamental knowledge in the field of physical education, developed a scientific worldview. Methodology. The development of scientific outlook of students of physical and mathematical directions of preparation, as a result of teaching IPDE, ensured the successful will be implemented in practice, such conditions as: 1. the involvement of experts in the field IPDE with teaching experience at the university; 2. development of the content of lectures and practical classes on the basis of modern achievements of the theory of inverse and incorrect problems, taking into account the professional orientation of training students; 3. the implementation of the principles, methods and means of education IPDE; 4. involvement of students in research work in scientific seminars and participation in scientific conferences devoted to IPDE; 5. implementation of methodological approaches that allow students to develop the skills and abilities of independent analysis of applied and humanitarian nature of the results of research of IPDE. Results. In practical classes on the IPDE students acquire the ability and skills to apply effective approaches and mathematical methods of finding solutions to inverse problems, followed by a logical analysis of their solutions. As a result, students gain useful experience in the analysis of new information about the studied physical processes and phenomena, form new scientific knowledge about the world on the basis of which develop a scientific worldview. Conclusion. Developed, in the process of teaching IPDE, the scientific outlook helps students to understand that mathematical models IPDE are relevant to theory, experiment and philosophy - the basic methods of knowledge researchers; to understand the humanitarian value of mathematical models IPDE.