New Perspectives in Science Education

Simultaneous teaching of thematically related methodological units requires a balance between online learning and in-person communications, which presents various technological, pedagogical, and organizational challenges. This paper is devoted to a new approach to simultaneously teaching several thematic mathematical units. The combination of improper integral and function investigation thematic units is used to compile a model of consideration. The main idea is based on the Partition of Unity Method for solving multistage problems. To this end, a set of appropriate problems is developed and classified. Multistage problems arising from the fractional Laplace operator are also created. A generator of problems related to the classical Basel problem is obtained by bilinear finite element transformations. In the current decade, insufficient time has been devoted to training undergraduate students in various majors to study functions defined by integral operators. Such tasks are usually left to the training of postgraduate students. This paper provides a different perspective on this issue..