Olga Chigiryova

The article proposes a method of presenting the topic "Application of power series for the approximate calculation of definite integrals". The authors consider a method that makes it possible to calculate the values of definite integrals when the antiderivative integrand is not explicitly expressed in terms of elementary functions. The typical tasks of homework with detailed solutions are given. The article will be useful for students as well as teachers of the relevant courses.

The article presents a method of presenting the topic “Solving boundary value problems for the Laplace equation for a circle and a ring by the method of variables separation” in the course “Equations of Mathematical Physics”. A brief theoretical information related to the use of variables separation method is given. The general scheme for solving boundary value problems for the Laplace equation for the indicated domains is shown. The main stages of solving are summarized in tables. Typical tasks of the homework are analyzed in detail. The content of the article will be useful for students, as well as for teachers of relevant courses.

The article presents a methodology for the presentation of the topic “Solution of the boundary value problem for Laplace equation on a rectangle using Fourier method” in the mathematical physics equations course of the Bauman Moscow State Technical University. These mathematical tools are widely used in physics, mathematical physics, electrodynamics, quantum mechanics, acoustics, wave optics, oscillation theory, theory of signals and circuits. The purpose of the work is to help students acquire the skills to apply the methods of mathematical physics to solving various physical tasks. One of the main methods of solving mathematical physics tasks is the Fourier method (separation of variables). The Sturm-Liouville problem is an important stage of this method. In order to structure the main types of Sturm-Liouville problems, the article contains information summary table. The article contains the basic theoretical information and an example of a solution of the boundary value problem for the Laplace equation on a rectangle. The article will be useful for students of instrument-making specialties, as well as teachers of the relevant courses.

The article describes the methodology of the topic "Generalized functions. Generalized derivatives. Delta-Dirac function" presentation in the course of equations of mathematical physics at MSTU named after N.E. Bauman. Delta function was introduced by physicists, trying to formally determine the density of point mass (point charge). Then it was used in the equations of mathematical physics, but without good mathematical reasoning. A general theory of generalized functions was later developed in the works by S.L. Sobolev and L. Schwartz. This mathematical tool is widely used in physics, mathematical physics, electrodynamics, quantum mechanics, acoustics, wave optics, theory of oscillations, the theory of signals and circuits, so it is necessary for students of instrument engineering specialties. However, its academic presentation makes considerable difficulties for the students. The aim of this paper is to propose methodology for academic presentation of generalized functions theory, intelligible to second-year students. Practical methods for calculating generalized derivatives are demonstrated. The article is written on the basis of broad experience in teaching mathematical physics equations and will be useful for students of instrument engineering specialties, as well as for teachers of relevant courses.

The paper proposes a technique for presenting the topic "The formula of full probability and the Bayes formula" based on the personal experience of the authors in the discipline "Theory of Probability". When solving problems on this topic, the greatest difficulty for students is calculation of conditional probabilities. In this connection, special attention is paid to the method of solving problems. The main theoretical information and a large number of typical examples showing solutions that allow students to acquire the necessary skills in mastering this topic are given.