Математика https://rep.ksu.kz//handle/data/9304 2022-08-17T21:57:33Z The implementation of interdisciplinary approach in teaching mathematics in the context of the updated content of education: monograph https://rep.ksu.kz//handle/data/12295 The implementation of interdisciplinary approach in teaching mathematics in the context of the updated content of education: monograph Kossybayeva, U.A.; Akhmanova, D.M.; Kazimova, D.A. The scientific work considers ways to implement interdisciplinary communication in the teaching of mathematics in the context of the updated educational content. The content of the monograph is aimed at defining the essence and functions of interdisciplinary communication in the program of high school mathematics by showing the STEM method and the use of information and communication technologies on the example of topics of equations and inequalities. The research is intended for high school maths teachers, university teachers and interested readers. 2021-01-01T00:00:00Z Singular Integral Equations for Heat Conduction Problems https://rep.ksu.kz//handle/data/10996 Singular Integral Equations for Heat Conduction Problems Kosmakova, M.T.; Orumbayeva, N.T. Currently, the use of contact equipment is constantly increasing. The experimental study of thermal processes is often difficult due to their transience. Therefore, in some cases, only a mathematical model can serve as the basis for obtaining additional information about dynamics of thermal processes. The monograph is devoted to formulation and study of boundary value problems for the heat conduction equation in non-cylindrical domain, the domain degenerates to a point at the initial time. The study is based on reducing the formulated problems to the second-order Volterra singular integral equation, and solving this integral equation. The methods for solving equations (when the upper and lower limits of integration coincide, the operator is not equal to zero) are not specific to ordinary Volterra equations, so they were called singular Volterra integral equations of the second kind. The monograph will be interesting to scientists, doctoral students, undergraduates, students, university teachers and everyone involved in the field of heat equations and integral equations. 2020-01-01T00:00:00Z Periodic solutions of boundary value problems for hyperbolic equations with a mixed derivative https://rep.ksu.kz//handle/data/9307 Periodic solutions of boundary value problems for hyperbolic equations with a mixed derivative Orumbayeva, N.T.; Kosmakova, M.T.; Keldibekova, A.B. The monograph is devoted to the study of periodic boundary value problems for systems of hyperbolic equations with a mixed derivative. The work proposes methods for finding approximate solutions of periodic boundary value problems for systems of linear hyperbolic equations. The coefficient characteristics of the unique solvability of the periodic boundary value problem for a system of linear hyperbolic equations are established. The definition of the isolated solution of a semi-periodic boundary value problem for the nonlinear system of the hyperbolic equations, generalizing definition of the isolated solution of nonlinear boundary value problems for ordinary differential equations are introduced. The criterion for the existence of a solution of a semi-periodic boundary value problem for systems of nonlinear hyperbolic equations in terms of the problem data is established. The main theorems of the work are illustrated by examples. The monograph is of interest to teachers, undergraduates and university students. 2019-11-29T00:00:00Z