Фізико-математичні науки. Випуск 18 161 each iteration. The efficiency of the developed method was illustrated by a computational experiment in a unit square for the case of the exponential dependence of the power of thermal sources on temperature. The results of the experiment are presented in the form of graphical (contour lines and the surface of an approximate solution) and numerical (values of an approximate solution at some points in the area) information.

The article considers the use of case-study method while studying of the topic “Equations with partial derivatives of the hyperbolic type” from the course “Methods of mathematical physics”. The requirements for the educational institutions are outlined in accordance with the concept of mathematical education in Ukraine. The emphasis is placed on the system-activity approach to the learning process. Attention is focused on the necessity to use the method of problem-based learning and one of its forms – the case method. There has been analyzed the concept of a case. There have been described the advantages of the case-study method and the system of requirements for it. There has been revealed the importance of choosing the topic “Equations with partial derivatives of the hyperbolic type” related to its applied nature. The article demonstrates the main stages of the research work of students of the Faculty of Physics and Mathematics in establishing the minimum conditions for the solvability of a mixed problem for a linear homogeneous hyperbolic equation. The paper also identifies and characterizes the main groups of results to be processed. The investigation indicates the selection criteria that help to establish the minimum conditions for the existence of a solution of a mixed problem for a linear homogeneous hyperbolic equation. The results of the research are presented in the form of a table. The research presents the main statements recognized as the best conditions corresponding to the set goal of the study. The originality of the method of proving statements and the skillful combination of two important topics of the course “Methods of mathematical physics” – “Equations with partial derivatives of the hyperbolic type” and “Integral equations” are noted. Application of the case-study method makes it possible to activate the learning process, to form positive motivation and to renew the creative potential of teachers. Proven research work within the course “Methods of mathematical physics” provides a solid basis for using the case method in the further professional activities of teachers. Along with this, the theoretical and methodical preparation of case technologies in institutions of higher education requires further improvement.