Irina Pelevina

This article proposes a version of presenting material on the subject “Laplace transform. Finding the image by the original” in a concise form. The main theorems are examined with the help of which images are found by originals and vice versa. Examples are chosen in such a way as to clearly illustrate each theorem and the basic concepts of the subject. The content of the article will serve as a material for the second year students’ classes preparation when they study the section “Operational Calculus” and will be useful to both teachers and students.

In this article, a version of the topic "Continuity of a function at a point" presentation is proposed. The necessary theoretical material is supported by examples. The tasks on this topic are selected in such a way that clearly illustrates the basic concepts of the topic. In addition, the selected tasks and examples represent methodological recommendations for homework doing and preparation for control work. The authors consider them as one of the students' education organizing forms and revealing residual knowledge on the topic. For convenience of the stated material perception, points of discontinuity classification is presented in the form of a table with illustration of typical examples. The content of the article will be useful for teachers and students.

The paper proposes a methodology for the presentation of a main section of mathematical logic – propositional logic. The authors consider a large number of examples, which explain the meaning of the basic definitions. The paper provides a table that summarized the operations disjunction, their meaning and examples. The paper can be useful to teachers and first-year students.

The paper deals with the method of the theme “Multivariate random variable” presentation in the course “Probability theory”. The paper is based on experience of teaching probability theory and it will be useful for both students and teachers for conducting practical classes. It lacks proof of theoretical facts, however, has a list of references that can be consulted for more detailed explanation. The work covers two examples: one for a discrete random vector, the other for a continuous random vector. These examples found the laws of distribution and main numerical characteristics studied in the course of probability theory. A structured approach to the material combining basic theoretical information and analysis of typical tasks will help students in independent and homework work.

The paper is devoted to teaching theory of limits in the course of mathematical analysis and the problems that arise in presenting educational material. To master the recording skills of the Cauchy function limit determination in the language «epsilon-delta», the authors propose a table that addressed all possible argument aspirations, written through the surroundings and intervals; provide definitions of the function limit for all cases reviewed in the table and explain in detail the content and meaning of these basic definitions on the examples of tasks. The authors offer the table that summarizes the uncertainties and shows the ways of their elimination. Calculation method of all kinds of limits on a wide range of tasks is also illustrated. The paper can be useful to lecturers and first-year students.