Faniya Ahmetova

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.

Free knowledge of charting techniques often helps to solve complex problems, and sometimes is the only way to solve them. In the article, the authors propose one of the methods for constructing curves of multivalued linear functions containing the modulus sign, namely, the method of splitting a function into separate equations. Brief theoretical information is given in the field of the functional dependence of multivalued functions. Practical methods of constructing curves of various complexity levels by the method of splitting a function into individual equations are demonstrated. The aim of the work is to systematize and deepen the knowledge of students, to give an algorithm for constructing curves of multivalued functions by methods and techniques that go beyond the school textbook of mathematics. The content of the article will be useful for students, as well as for teachers working with first-year students.

The task of results graphical presentation is sometimes complicated, because it does not always lead to the construction of a graph, which can be quickly depicted on a plane with high quality. The article proposes one of the methods for constructing graphs of multi-valued linear functions containing the modulus sign, namely, the method of splitting the coordinate plane into several areas. Brief theoretical information in the field of functional dependence of multi-valued linear functions is given. The authors demonstrate practical techniques that allow constructing sketches of functions graphs of various complexity levels by the method of plane splitting. The purpose of this work is to give an algorithm for constructing graphs of multivalued functions containing the modulus sign; to show the effectiveness and easiness of constructing graphs using the specified method. The content of the article will be useful to students, as well as to teachers working with the first-year students.

The article proposes a method of presenting the topic “Constructing graphs of multivalued linear functions containing a modulus sign” in the course “Mathematical Analysis”. A brief theoretical information in the field of functional dependence of multivalued linear functions is given. The authors demonstrate practical methods to build the sketches of functions graphs with different levels of complexity. The purpose of this work is to give an algorithm for constructing graphs of multivalued functions, containing a modulus sign, to which linear transformations are applied. The content of the article will be useful for students, as well as for teachers working with the first-year students.

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.