In the article, the authors consider the problems of improving the methodological training of future mathematics teachers in the practical lessons of the subject "Methodology of teaching mathematics". For the professional orientation of the teaching, some problems with algorithms for finding derivative functions and the tangent equation for the function were used in the practical lessons in the subject ―Mathematical Analysis‖. Methods of using algorithms in solving problems of finding derivatives and using the tangent formula for a function were developed.
Different methods of solving the problems of acquiring and deepening the concept of integral and problems of using integrals are given. Appearance of nonlinearity due to nonlocality in diffusion through fractured-porous media at multiple scales // Computational Geosciences.
УДК 517.956
The study of the stability of the closed-loop control system and the solution of the problem of the synthesis of the controller (determining the coefficient of the size matrix) and the observer (calculation of the matrix elements of the observation device) are based on direct Lyapunov methods. In this paper, we develop an algorithm for the numerical solution of the direct problem for the Helmholtz equation. The aim of this paper is to find an approximate solution of the direct problem for the Helmholtz equation.
THE CONSTRUCTION OF THE GREEN'S FUNCTION IN THE TWO-DIMENSIONAL DIMENSION FOR THE BIHARMONIC EQUATION. Green function representation for the Dirichlet problem of the polyharmonic equation in a sphere // Complex variables and Elliptic equations.
ГРНТИ 27.01.45
The technology of creating the content of the subjects of the science cycle in the development of students' mathematical literacy is discussed. INNOVATIONS IN MATHEMATICS EDUCATION - NEW METHODOLOGICAL TECHNOLOGIES Ilyasova R.A. Pedagogic), professor at the Kazakhstan State University for the Training of Female Teachers, Almaty, Kazakhstan. At a fixed value of the parameter, the Cauchy problem for the loaded differential equation is solved.
The existence of the solution of this system ensures the solvability of the problem under study. The numerical implementation of the proposed algorithm is based on the use of Taylor series in solving the Cauchy problem for ordinary differential equations.
Кіріспе.Cолитондар арасындағы ӛзара әсерлесуді зерттеу ғылымда үлкен рӛл атқарады [1-2]
A mathematical model is used to describe the course of a disease in a group of people. The use of a numerical method makes it possible to predict the course of the disease. A computer algorithm is proposed for solving the problems of predicting the course of a disease in a group of people.
This group of people is divided into three subgroups, which describe the different stages of the development of the disease. The work presents graphs describing the change in the number of people in each of the three subgroups considered. Mathematical modeling is one of the investigative methods used to study processes in epidemiology.
2 shows the change in the number of people in group I (infected at time t) over 5 days. The graph in figure 2 shows that the number of infected people increases during the first 2 days with a further decrease and stabilization of the number of people in this group. 3 shows the change in the number of people in the R group (who had recovered at time t) over 5 days.
4 shows the change in the number of people in group S (healthy at time t) for 3 days. 5 shows the change in the number of people in group I (infected at time t) for 3 days. In the second variant, the dynamics of changes over time in the number of people in the considered groups remains the same as in the first variant.
УДК 517.925
- Построение начальных функций. Рассмотрим функцию Коши [1]
- Построение граничных функций. Введем в рассмотрение граничные функции
- Построение решения краевой задачи. Справедлива следующая теорема
- Дифференциальные свойства минимизируемого функционала
3 Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan ASYMPTOTIC EXPANSION OF THE SOLUTION OF THE CAUCHY PROBLEM. An asymptotic estimate of the remaining term of the Cauchy problem solution is obtained. 6 Akhmet M.U., Buyukadali C. Periodic solutions of a system with a partially constant argument in the critical case.
An asymptotic estimate of the remaining term of the Cauchy problem solution is obtained. The fundamental system of solutions of the homogeneous equation of the boundary value problem is constructed. An analytical representation of the solution of the original singularly perturbed boundary value problem is constructed.
THEORETICAL CHARACTERISTICS OF THE FUTURE TEACHER PREPARATION FOR THE FORMATION OF FUNCTIONAL LITERACY OF PRIMARY SCHOOL STUDENTS IN INTEGRATED EDUCATION. To solve this problem, it is necessary to develop and test a technology for the development of the teacher's professional competence in developing the functional literacy of students in the integrated teaching of mathematics and physics. To identify trends and conditions for the development of teacher professional competence in the formation of students' functional literacy.
Theoretical substantiation of the content of the professional competence of the teacher in the formation of functional literacy of students. To develop and test the technology for the development of teacher professional competence in the formation of functional literacy of students in the integrated education of mathematics and physics. The methodological basis of the research is based on three levels (general philosophical, general theoretical, specific scientific).
Develop and test an interactive technology for the development of the teacher's professional competence in the formation of functional literacy of students in the integrated teaching of mathematics and physics, including the stages of goal setting, planning, prediction, implementation, correction, reflection;. Development of the teacher's professional competence in the formation of functional literacy of students includes [8,9,10]: the goals to increase the professional competence of the teacher; training program;.
Пусть
- Рекуррентные формулы для численного решения краевой задачи (1)–(3), в случае когда
- Рекуррентные формулы для численного решения краевой задачи (1)–(3) в случае когда
- Рекуррентные формулы для численного решения краевой задачи (1)–(3) в случае, когда
ALTERNATIVE AND EXTENDED OPTION OF THE METHOD FOR PROTONING THE NUMERICAL SOLUTION OF THE 1ST LIMIT PROBLEM FOR LINEAR DIFFERENTIAL EQUATIONS. In this article one finds recurring formulas for classical sweeps analogous to formulas (Thomas' algorithm in the English literature), for the numerical solution of the second and third boundary value problems of second-order differential equations, when the commonly used method of sweeping can lead to disappointing results . In particular, cases are considered that are particularly important: sweep formulas, when the comparison coefficient (has a negative or alternating sign) and the boundary conditions do not meet the conditions of computational stability of the commonly used sweep method.
As a result, a new algorithm is proposed which is an alternative to the sweep method for the numerical solution of second-order linear differential equations with fixed boundary conditions. The obtained formulas can be used for the numerical solution of the initial boundary value problem with discontinuous coefficients. The algorithm is tested on specially selected numerical examples that reflect the characteristic features of the investigated boundary value problems.
Таким образом, чередуя формулы обратного движения для отрицательного «входа» (9) и положительного «входа» (10), можно найти все искомые значения yn, (n=N1,..1.). Далее организация этого численного процесса обратного движения полностью аналогична предыдущему случаю, то есть, чередуя формулы обратных движений для отрицательного «и положительного» входа, можно получить все интересующие значения yn 1. , (n=N,N1,..1 .). Настоящая работа посвящена решению задач исследования почти многопериодного решения интегро-дифференциальных уравнений.
In addition, questions about the existence and uniqueness of an almost multiperiodic solution of a system of first-order integrodifferential equations in partial derivatives are considered. These results will also be useful in the study of nearly periodic solutions of the evolution equations of mathematical physics. Conditions (N ) relative to t x ensure the existence and uniqueness of the solution of the Cauchy problem to equation (3).
ФИЗИКА, ФИЗИКАНЫ ОҚЫТУ ӘДІСТЕМЕСІ
ФИЗИКА, МЕТОДИКА ПРЕПОДАВАНИЯ ФИЗИКИ
ALL SOLUTIONS OF THE INVERSE PROBLEM FOR THE HEAT CONDUCTIVITY EQUATION WITH NONLINEARITY SCALE. Physics-Math), Senior Lecturer, Kazakh National University al-Farabi, Almaty, Kazakhstan. Mathematical modeling of many processes occurring in the real world leads to the study of direct and inverse problems for the equations of mathematical physics. The theory of inverse problems is an actively developing branch of the modern theory of differential equations.
A special place in the theory of nonlinear equations is the series of studies of unbounded solutions, or, as it is otherwise called, regimes with peak points. In this paper, we consider an inverse problem with an integral condition of redefinition for an equation of parabolic type, and we obtain sufficient conditions for the destruction of its solution in a finite time in a bounded domain with a homogeneous Dirichlet condition. Inverse problem for non-stationary system of magnetohydrodynamics //. K. Solvability of the inverse problem for a heat convection system with integral condition of overdetermination // Applied Mathematical Sciences.
18 Эден А., Калантаров В.К. О несуществовании в мире решений обратной задачи для полулинейных параболических уравнений // Ж. 19 С.Гур, М.Яман, Ю.Йылмаз Взрыв решений обратной задачи для квазилинейного уравнения за конечное время. параболическое уравнение с силовой нелинейностью // Ладыженская Ю. О возникновении коллапсов для квазилинейных уравнений параболического и гиперболического типов // Зап. Высшее учебное заведение - это учебное заведение, в котором, помимо подготовки высококвалифицированных кадров в данной области, проводятся исследования в различных областях науки и техники. Ухудшение состояния окружающей среды, особенно загрязнение воздуха городов промышленными и транспортными средствами, направлено на детальное изучение процессов горения в промышленных отраслях.
Within the walls of the university, during the educational process and as final work, students conduct research on the combustion processes of various fuels. The Urysohn integral equation is considered in the Banach space BC (R +), consisting of real functions defined, continuous and bounded on R. The result of the research in the article is formulated with a theorem and the proof of the existence theorem is given as the solution of the quadratic Urysohn integral equation in the Banach space BC (R +).
