Anna Kosova

This article proposes a method for presenting the topic “Solution of the Cauchy problem by method of incorporating initial conditions into instantaneous sources” in the course of mathematical physics equations. The Cauchy problem is considered in a generalized formulation, which allows us to get rid of cumbersome calculations that appear under nonzero initial conditions and distract from the essence of the problem. This article presents a method for solving the Cauchy problem, based on the use of a fundamental solution. The article is based on a wide experience in teaching mathematical physics equations and may be useful for students of instrument-making specialties, as well as for teachers of relevant courses.

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".

In this article, we propose a version of the topic "First-order differential equations" theoretical material presentation. The tasks on this topic are considered. The article deals with the frequently occurring errors of students. Particular attention is paid to building algorithms for solving first-order differential equations. Four basic types of equations are analyzed in detail in this paper: equations with separating variables, homogeneous, linear and Bernoulli's equations.

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, we propose a version of the material on the subject "Vector algebra." For convenience of perception, the theoretical part is presented in the form of a table. The tasks on this topic are selected in such a way that, when solving them, students should use all the studied material. Particular attention is paid to the upbringing of students' self-control in the process of solving problems.