This article overviews difficulties and challenges faced by mathematics professors and students at the Riga Technical University due to the necessity of enforced and immediate transition from the classroom to distance learning. It also contains research focused on finding an optimal way of teaching mathematics when only distance education is available. The research is based on surveys completed by students and mathematics professors about the experience gained during the spring and autumn semesters of 2020. The methods found through the research can be applied in teaching related subjects such as natural sciences and engineering.
Abstract. An analytical solution has been obtained for a problem on magnetohydrodynamic flow in a rectangular duct with perfectly conducting Hartmann walls and side walls of finite conductivity. The slip boundary conditions for velocity were applied to the duct side walls. The exact analytical solution of the problem has been obtained in the form of convergent series. On the base of the obtained analytical solution the velocity field of the flow has been studied numerically.Keywords: MHD duct flow, slip boundary condition. IntroductionA flow of electrically conducting fluid in the presence of external magnetic field produces a variety of new effects, which are not realizable in usual hydrodynamics. These effects are studied by magnetohydrodynamics (MHD), the discipline combining the classical fluid mechanics and electrodynamics.Electromagnetic methods of action on electrically conducting medium are widely exploited in industrial processes in metallurgy, material processing, chemical industry, industrial power engineering and nuclear engineering in order to control and manipulate various conducting materials. Besides, the MHD effects are exploited in technical devices such as MHD pumps, flow meters, MHD generators and accelerators, where channels with electrically conducting fluids are their common parts. Thus, investigation of MHD phenomena in channels with conducting fluids is quite important.In magnetohydrodynamics the number of exact analytical solutions is limited due to the nonlinearity of the Navier-Stokes equations. Therefore, numerical methods are widely used for solving these problems, although analytical solutions still do not lose their importance (even if these solutions are often obtained for simplified flows). The present analytical study was motivated by the recent publication [2], in which three classical MHD problems were considered, but the applied boundary condition at the interface between the electrically conducting fluid and the insulating solid walls was the hydrodynamic slip condition. Despite the no-slip boundary condition is usually applied for the majority of flows of viscous fluids, there exist situations when no-slip boundary conditions lead to unrealistic behaviour, for example, if viscous effects at the wall are negligible, then the slip boundary condition must be applied (see [1; 2]). This paper presents an exact analytical solution obtained for a new problem on a MHD flow in the rectangular duct with perfectly conducting Hartmann walls and the side walls of finite conductivity. The boundary condition applied to the Hartmann walls of the duct is the Dirichlet (no-slip) boundary condition, which is the simplest boundary condition for the velocity of viscous fluid, while the boundary condition applied to the side walls is the 3rd kind (slip) boundary condition. This solution seems absent in literature. Some numerical results for the velocity of the flow calculated on the base of the obtained analytical solution are also presented. It is to be noted that the study of the present prob...
Abstract. In a changing world, people's needs for education are also changing, so questions about improving the education system and the quality of education are particularly appropriate and important. Taking into account the changing educational needs of students and the fact that knowledge is becoming more universally accessible, we wanted to analyze our own learning processes and ask ourselves: "What is it that we want to provide as educators?" Students are directly interested in the quality of their studies. A confident and supportive approach to the 1st year students during math lessons is an important factor in raising the interest of students in mastering higher mathematics. This will assist students in developing their ability to solve engineering problems in the future. Student surveys are one of the most commonly used instruments in higher education institutions for collecting a reasonable student assessment of various indicators, characterizing both the quality of the studies and the lecturer's professional work. It is the potential of such surveys, which aim to improve Mathematical studies through knowing what students really think, and to gain an understanding what can help them to learn mathematics better, that prompted us, several Professors of Mathematics of the Department of Engineering Mathematics, to create our own survey with questions, which are specific to Mathematical subjects. The survey results are very informative. The structure of the survey invites students to extend their "yes"/ "no" answers with details, comments and opinions, and these are the most valuable results of the survey.
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