Humanitarian knowledge in the learning content to the inverse problems for differential equations

Problem and goal. Currently, humanitarization is a trend in the development of many scientific and educational fields, among which, undoubtedly, is applied mathematics. The significant contribution of applied mathematics to the development of human civilization is obvious. At the same time, it is widely known that in some cases the practical implementation of applied research entails global environmental problems. There are irreversible negative processes in the environment. Such situations inevitably lead to a contradiction between the modern achievements of world science and its social and moral aspects. This problem is recognized not only by scientists. It is no coincidence that one of the directions of improvement of the Russian education system is the humanization of mathematical education, the concept of the content of which has been developed since the nineties of the last century. One of the aspects of humanitarization of mathematical education is ecological education of students. A certain contribution to the formation of environmental education of students of physical and mathematical specialties of universities makes teaching inverse problems for differential equations, the content of which is formed on the basis of the theory of inverse problems for differential equations. In this connection, in the process of teaching inverse problems for differential equations are realized such goals as: familiarity of students with the basics of humanitarian analysis of applied research, teaching students to formulate their own logical conclusions of applied and humanitarian character on the results of the study of the inverse problem for differential equations. Methodology. The achievement of the above mentioned didactic goals of teaching inverse problems for differential equations is largely provided by how successfully will be implemented in practice such didactic learning tasks as: 1. realization of humanitarian potential of teaching inverse problems for differential equations; 2. formation of students’ skills and abilities of independent analysis of applied and humanitarian nature of the results of the study of inverse problems for differential equations; 3. substantiation of the role of applied and computational mathematics in the development of human civilization. In addition, in the process of teaching students inverse problems for differential equations it is advisable to implement a system of humanitarian-oriented training sessions. This is due to the fact that in the process of such training students acquire fundamental knowledge not only in the field of mathematical methods of research of such applied problems. In the process of learning the inverse problems students are instilled features of humanization. Results. In the process of teaching inverse problems for differential equations, students acquire the ability and skills to analyze the solutions of inverse problems, to formulate logical conclusions about the ecological state of the air space, the earth’s environment or the aquatic environment, to apply numerical results of solutions to inverse problems in the humanitarian analysis of applied research. Conclusion. Fundamental knowledge in the field of inverse problems for differential equations, skills of using this knowledge in their professional activities, the possession of humanitarian culture, awareness of the humane relations of their applied activities with the environment and society contributes to the formation of students’ spirituality, the development of worldview and awareness of involvement in the civilized development of society.