Keyword: «laplace equation»

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 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.