Tatyana Laskovaya

In this article, a basic scheme of proving theorems from definition to final assertion is considered. A template for decoding the definition of the limit of a Cauchy function is proposed. A special attention is paid to the link between theory and practice considered on specific tasks and theoretical conclusions of formulas. The methodological approach to the presentation of the theory is illustrated by the topics of the course "Mathematical Analysis".

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.

This article proposes a version of the theoretical material on the topic “Linear differential equations with constant coefficients and the right-hand side of a special form” in a short form. The tasks on this topic are considered. Particular attention is paid to the analysis of the most common mistakes of students in solving the tasks. Various ways of material presentation of are considered.

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.

In work the method of presentation of the topic "Functions of random variables" in the course "Probability theory". The article is written based on years of experience teaching this subject and will be useful for both students and teachers in conducting practical classes. There are no proofs of the theorems used, however, a list of references that can be consulted for more detailed explanations. Considered a large number of examples that will allow students to learn the material under study to the extent necessary. The aim of this work is to help students to acquire skills in the application of probability methods to the solution of various problems.