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Master degree program

Mathematical and Computer Modelling

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Master degree program
Educational programs
Mathematical and Computer Modelling

Mathematical and Computer Modelling

QUALIFICATION

Scientific and pedagogical direction - Master of Engineering Sciences

MODEL OF GRADUATING STUDENT

ON1. Conduct research and obtain new fundamental and applied results, plan research in accordance with the approved direction of research in the field of specialization. Apply modern methods of mathematical modeling for scientific research.
ON2. Use the concepts of the essence, mechanisms and patterns of natural-physical, chemical-technological, natural, biological, medical and random processes in the development of conceptual and theoretical models of solvable applied problems.
ON3. Use high-performance computing systems and methods of mathematical and computer modeling in the analysis and solution of applied problems.
ON4. To draft and develop recommendations for the implementation of the research and numerical experiments in the production and financial industry using mathematical and computer simulation methods. Use probabilistic methods to solve actual problems of mechanics, physics, and economics.
ON5. To carry out an in-depth analysis of problems, to produce a substantiation of physical problems, to reveal their natural-scientific essence in the course of scientific and research activities, to apply the corresponding mathematical apparatus and a numerical algorithm to solve them.
ON6. Create mathematical models and apply numerical methods for solving problems of heat and mass transfer with a moving boundary, inverse and ill-posed problems of mathematical physics, biomedical processes, natural-physical processes, chemical processes, financial processes, atmospheric processes, dynamics of multiphase turbulent flows.
ON7. Analyze, design and conduct numerical experiments of constructed mathematical models of industrial, physico-technological, non-linear non-stationary physical, chemical, biomedical, financial processes. Reproduce numerical solutions of engineering problems of hydrodynamics on high-performance systems
ON8. Conduct scientific research in the field of mathematical modeling of heat and mass transfer phenomena, continuum dynamics, thermal and complex processes, mechanical processes, thermodynamic processes in gas dynamics, thermodynamic and electrical processes in solids, applied problems, problems of mathematical physics, and stability theory in economics and technology.
ON9. Apply mathematical and numerical apparatus to research in the field of financial mathematics, computational hydrodynamics, mechanics, turbulence modeling, physical, chemical, biomedical, nonlinear nonstationary physical processes and complex systems for solving applied problems.
ON10. To conduct educational and extracurricular work, have the skills of pedagogical activity. Conduct lectures, seminars and laboratory classes for undergraduate students on the profile of the specialty. To master and introduce new innovative technologies and approaches in the field of education in teaching practice.
ON11. Conduct research to use the results obtained in the framework of the implementation of interstate programs in the field of mathematical modeling, mathematics, biomedicine, physics, chemistry and mechanics. Participate in scientific seminars and conferences.
ON12. To work in a team, tolerantly perceiving social, ethnic, confessional and cultural differences, critically evaluate one’s activity, team one’s activities, outline ways and choose means for self-development, improvement of one’s qualifications.

Program passport

Speciality Name

Mathematical and Computer Modelling

Speciality Code

7M06106

Faculty

Mechanics and Mathematics

disciplines

Foreign Language (professional)

History and Philosophy of Science

Mathematical and computer modeling of medical and biological processes

Mathematical modeling in computer graphics

Modern methods of computational fluid dynamics

Number of credits - 5
Type of control - [RK1+MT+RK2+Exam] (100)
Description - Thepurpose of the discipline: to form students' ability to apply modern methods of numerical solution of hydrodynamic equations, practical application of the main stages of mathematical modeling of hydrodynamic processes, including the physical formulation of the problem, the choice of a mathematical model and the formulation of the initial-boundary-value problem, the construction of a network model, the choice and development of grid approximations, teach the construction of various algorithms for constructing finite difference and finite element meshes.. During the study of course, master students should be competent in: – applyingthe methods for the numerical solution of the Navier-Stokes equations in the case of an incompressible fluid on a spaced grid; – applying solutions to viscous compressible fluid; – building end-to-end counting schemes, explicit and implicit methods for solving initial equations; – applying the McCormack method, the Bima-Warming method, TVD schemes; – applying the high order schemes - ENO and WENO. During the study of the disciplines, master tudents will learn following aspects: methods for the numerical solution of the Navier-Stokes equations in the case of an incompressible fluid on a spaced grid. The solution methods for a viscous compressible fluid, hyperbolic systems, conservation laws, and problems of their solution are studied; cross-counting schemes, explicit and implicit methods for solving initial equations; McCormack method, Bim-Warming method, TVD schemes (monotonous reconstruction, slope limiters). High order methods. ENO and WENO.

Modern methods of mathematical modeling

Modern technologies of parallel programming

Pedagogy of Higher Education

Psychology of management

Data for 2021-2024 years

disciplines

Computer modeling and vizualization in graphic paсkages

Development and research of methods of modeling the behavior of complex processes

Type of control - [RK1+MT+RK2+Exam] (100)
Description - The purpose of the discipline: is the formation of knowledge and skills in creating and exploring mathematical simulation models of complex processes and systems. During the study of course, master students should be competent in: - to demonstrate deep knowledge of the current state and trends in the development of scientific knowledge in the field of mathematical modeling of complex processes; - to consider complexes of mathematical models of the behavior of complex processes; - use theoretical and experimental studies to simulate complex processes; - develop algorithms and software for managing complex processes based on research; - to generate the received scientific knowledge in own scientific research. During the study of the discipline master students will learn following aspects: Models of data structures; understanding of DBMS classification methods depending on implemented data models and methods of their use; studying the ways of storing data at the physical level, the types and methods of organizing file systems; detailed study of the relational data model and DBMS implementing this model, the language of SQL queries; An understanding of the problems and the main ways to solve them with the collective access to data; study of the capabilities of DBMS supporting various models of data organization, advantages and disadvantages of these databases in the implementation of various data structures, the means of these DBMS; understanding the stages of the life cycle of the database, support and maintenance; Obtaining an idea of specialized hardware and software tools oriented to building databases of large volumes of storage.

Development of mathematical models of control of multidimensional phase systems

Direct methods for modeling turbulence problems

Type of control - [RK1+MT+RK2+Exam] (100)
Description - The purpose of the discipline: to form the ability to develop high-order accuracy methods for the numerical solution of a three-dimensional turbulent flow system; direct numerical simulation of three-dimensional transitional and developed turbulent flows; a detailed study of the mechanisms and evolution of transition and turbulent flows. During the study of course, master students should be competent in: - developing a class of stable difference schemes of high order of accuracy for the direct numerical solution of three-dimensional turbulent flow. - simulating various physical processes with different schemes of calculation of the coefficient of turbulence; - making a comparison of calculations using the proposed model with observational data$ - studying the structure and parameters of currents in the transition region and the region of developed turbulence, to obtain statistical characteristics of turbulence. - conducting detailed numerical studies of the structure and parameters of three-dimensional transient and turbulent flows, as well as the stages of the turbulent flow evolution: vortex formation and associated oscillations of gas-dynamic parameters, interaction of vortices in the flow, their dissipation and transition to the developed turbulent flow. During the study of the discipline, master students will learn following aspects: construction of a mathematical model for various physical processes; the correct choice of the algorithm of parametrization of turbulent exchange; construction of difference schemes and algorithms for solving problems; construction of flowcharts for numerical algorithm and program code; analysis of the results of numerical simulation of various turbulent flows.

Elements of the theory of sustainability in economics and technology

Type of control - [RK1+MT+RK2+Exam] (100)
Description - The purpose of the discipline: to form fundamental knowledge in the theory of stability, theoretical and scientific-practical problems of sustainable development of economic systems. During the study of course, master students should be competent in: - describe the basic concepts and methods of the theory of stability - to demonstrate the idea of Lyapunov stability and asymptotic Lyapunov stability and asymptotic stability -to investigate solutions for Lyapunov stability and asymptotic stability by linear approximation of solutions of differential and difference equations, -to be able to depict phase portraits of a second-order linearized system both in the case of a system of differential and in the case of a system of difference equations. During the study of the discipline, master students will learn following aspects: The concept of sustainability in the economy. The development of the theory of sustainability of economic systems. The main elements of economic sustainability. Introduction to the theory of sustainability in engineering. Stability of linear systems. Basic concepts of the theory of sustainability. General theorems on the stability of linear systems. Stability of linear systems with a constant matrix. Development of the conceptual concept of a particular type of sustainability under study. Definition of methodological features and methods for determining the stability of this type. Development and justification of a system of quantitative indicators determining the stability of the economic system. Evaluation of the specific features of the investigated object of sustainability, i.e., enterprises (taking into account its specialization, affiliation with a particular industry, regional characteristics of economic activity, size of economic potential, development opportunities, etc.). Carrying out the necessary calculations, analyzing the results obtained on the example of a real object and the adjustment of the originally developed methods. Testing the mechanism of managing the stability of the studied economic system.

Finite element method in applied problems

Formal methods of software development

Type of control - [RK1+MT+RK2+Exam] (100)
Description - The purpose of the discipline: to form the student a set of knowledge and skills related to the design and development of industrial software; the study of existing design methods and the current regulatory framework; the development of modern technologies for the development and implementation of software projects, as well as the fundamentals of project management. During the study of course, master students should be competent in: - methods of design and development of industrial and embedded software; - modern technologies for the implementation of software projects and related standards; - specifics of designing and developing software for highly efficient metamodels and multidisciplinary optimization systems; - develop software projects for industrial and embedded systems in compliance with domestic and foreign standards; - implement effective implementation of software projects in key executive and management positions; - apply model projects and practices as a basis for their own unique software solutions; - To make a risk assessment and consciously choose the best approaches and technologies for developing, testing and maintaining software; - skills of setting research tasks and skills of independent work. During the study of the discipline, master students will learn following aspects: general methodology and organizational and technical support of work. A brief overview of the history of technologies and software development methods in domestic practice and abroad. Classification of software systems: distinctive features, quantitative factors. Features of the design of industrial and embedded software. Software development based on formal methods (Cleanroom). Flexible development methodologies (Agile, Scrum, XP, MSF). Visual programming technologies (RAD). Software life cycle and its regulatory framework. The main stages of the design and development of software within the known models. Project Processes. Technical aspects of development. The choice between procedural, data-oriented and object-oriented approaches in the development of industrial and embedded software. Algorithmization and selection of an efficient algorithm, taking into account the characteristics of computational complexity. Use existing software code. Development of firmware and real-time software systems. The use of OpenMP and CUDA parallelization technologies in embedded systems.

High performance computing technologies

Type of control - [RK1+MT+RK2+Exam] (100)
Description - The purpose of the discipline: to form knowledge about the basic architectural concepts of building high-performance information processing facilities; macrostructure of large-scale distributed computing systems (VS); functional structures and the most interesting industrial implementations of high-performance computing systems. During the study of course, master students should be competent in: - explain the key concepts and principles of the organization of parallel computing. - to demonstrate the main trends in the development of parallel architectures, factors affecting performance, criteria for choosing a software and hardware platform for solving computationally-complex tasks of a given class. - to master the general methodology for developing parallel programs, methods for evaluating the effectiveness of parallel algorithms and the maximum attainable parallelism on the target computing architecture. - be able to use the means of remote access to computing resources for collective use and launch of parallel programs on computing clusters. -the ability to generate new ideas and demonstrate the skills of independent research work and work in a research team; - the ability to conduct research and obtain new scientific and applied results; - ability to develop conceptual and theoretical models of solvable scientific problems and tasks; - the ability of in-depth analysis of problems, formulation and justification of the tasks of scientific and design-technological activities. During the study of the discipline, master students will learn following aspects: Problem, object and object orientation of high-performance computers and computing systems. Specific requirements for them. Single-processor and multiprocessor systems; multiprocessor systems with shared memory and local memory; parallel and distributed computing systems. Classification systems of supercomputers. Performance evaluation of high-performance computers and computing systems. Amdal's law, theoretical and real productivity growth in parallel computing. Principles of development of parallel methods. Simulation of parallel programs. Simulation of mass transfer processes.

Mathematical and computer modeling of chemical processes

Type of control - [RK1+MT+RK2+Exam] (100)
Description - The purpose of the discipline:is to improve the professional training of the student in the field of modeling of chemical and technological processes, includes master degree students knowledge in the field of modeling, compiling and optimizing mathematical models, using modern mathematical software packages in modeling; formation of professional skills in modeling chemical and technological processes, in the analysis and processing of data using modern information technologies. During the study of course, master students should be competent in: - building mathematical models of the systems under study; - carrying out analytical research and optimization of the developed mathematical model; - realizing the developed mathematical models in computer form; - applying the methods of computational mathematics to solve specific problems of the processes of chemical technology; - knowing methods of constructing a mathematical model of typical professional problems and a meaningful interpretation of the results obtained; - using packages of applied programs for modeling of chemical and technological processes. During the study of the discipline master students will learn following aspects: The course is designed to expand the knowledge of basic concepts, techniques and methods of mathematical and computer modeling, consideration of modern technologies for constructing and researching mathematical models for chemical-technological processes. The course discusses the principles of the formation of mathematical models, methods for constructing physico-chemical models of chemical-technological processes, types of reactors and chemical-technological processes, methods for optimizing chemical-technological processes using empirical and / or physico-chemical models.

Mathematical and computer modeling of meteorological problems

Mathematical and Computer Modeling of Unsteady Nonlinear Physical Processes

Mathematical modeling of thermophysical processes in multilayer environments

Type of control - [RK1+MT+RK2+Exam] (100)
Description - The purpose of the discipline: is the development and research of a complex of mathematical models for solving heat and mass transfer problems in automatic process control facilities, developing control systems for thermophysical processes in such conditions for obtaining high-quality, reliable products from composite materials and developing recommendations for improving technology. During the study of course, master students should be competent in: - identify specific requirements, opportunities and problems in the development of a mathematical model of thermophysical processes in multilayer environments; - systematize and interpret scientific theories and concepts of the latest trends in mathematical and computer modeling; - apply general programming knowledge in the field of computer modeling; - critically evaluate the results of scientific research, modern theories, problems and approaches, new trends in the study of thermal processes in multilayer environments; - to differentiate the priorities of educational and research activities, correlating their own scientific interests with social, ethnic values, the needs of production and society. - present the results of educational and research activities in the form of scientific reports, abstracts, abstracts of articles, physical and mathematical comments, master's theses. During the study of the discipline master students will learn following aspects: Identification of physico-chemical factors that determine the temperature fields in the process of polymerization of composite materials and their accounting in mathematical models. Statement and solution of mathematical problems describing the temperature fields in the process of polymerization in the automatic recycling plant with regard to phase transitions and multi-stage.Development of finite-difference schemes and calculation of spatio-temporal distributions of temperature fields in the automated process control system.Analysis of the contribution of various processes to the temperature fields in the automated process control system and the development of algorithms and programs for managing thermophysical processes, the development of new installations (devices) for automatic control systems at all stages of product manufacturing. Development of a methodology for identifying during the process of manufacturing the sources of the degradation process. Identify the effeerature, time, heating rate and pressure on the quality of the material being manufactured.Development of recommendations for the management of the polymerization process in the automated process control system.

Mathematical models of the theory of elasticity

Methods for solving inverse and ill-posed problems of mathematical physics

Methods of generalized functions and boundary integral equations in theproblems of thedynamics of elastic structure

Type of control - [RK1+MT+RK2+Exam] (100)
Description - The purpose of the discipline: is the formation of students: to formation of the knowledge from the theory of generalized functions necessary to solve problems of the dynamics of elastic media. The statements of nonstationary boundary value problems for second-order differential equations are considered. Acquaintance with the construction of dynamic analogs of the Green and Gauss formulas in the space of generalized functions, obtaining their integral representations. During the study of course, master students should be competent in: – using the main types of special functions, their integral representations, asymptotics for solving problems of mathematical physics, –applying the theory of generalized functions to the solution of applied problems of mathematics and programming. – applying into practice the methods and techniques for solving the problems of the theory of elasticity, the theory of plasticity using different criteria of plastic flow; – using the laws of nonequilibrium thermodynamics of a continuous medium for the formulation and study of the problem statements of continuum mechanics; – knowing the practical techniques and methods of solving problems of mechanics of continuous media. During the study of the discipline students will learn following aspects: Boundary value problems for differential equations of the 2nd order. Construction of dynamic analogs of the Green and Gauss formulas in the space of generalized functions, obtaining their integral representations. Fundamentals of the integral Fourier and Laplace transforms in the space of generalized functions and methods for constructing solutions of partial differential equations. Generalized functions of one variable, operations with them. Generalized functions of many variables, operations with them.

Modeling of heat and mass transfer processes in electrical contacts

Modeling of the Gas Dynamics

Type of control - [RK1+MT+RK2+Exam] (100)
Description - The purpose of the discipline: the formation of students' knowledge in the areas of theoretical and applied gas dynamics. The course examines the elements of thermodynamics, the equations of state of perfect and real gases, the laws of conservation and the ratio on strong discontinuities, the ratio of parameters on an oblique jump, the change in entropy. The method of characteristics for the equations of gas dynamics, one-dimensional unsteady gas flow. During the study of the discipline master students will learn following aspects: –deriving the basic equations of gas dynamics in integral and differential forms. –understanding the equations of state of perfect and real gases. –explaining the surface of a strong and weak rupture on the basis of a one-dimensional gas flow. –carrying out the derivation of the parameter ratios on an oblique jump, to explain the change in entropy. –using the characteristic method for two-dimensional stationary supersonic gas flow. During the study of the discipline, master students will learn following aspects: Gas dynamics methods, gas dynamics model. Basic equations in integral and differential forms. The problem of the spread of sound. The speed of sound Mach number. One-dimensional stationary gas flow. Laval nozzle. Basic equations in integral and differential forms. Direct shock wave, change of parameters of gas at transition through a direct jump. Oblique shock wave. Ratios of parameters on an oblique jump, change in entropy. Loss of total pressure. dependence of the angle of inclination of the oblique jump on the angle of rotation of the flow. Two-dimensional stationary supersonic gas flow. Characteristic method for irrotational flow. Small perturbation theory.

Modeling of the physical processes in the heterogeneous environments

Type of control - [RK1+MT+RK2+Exam] (100)
Description - The purpose of the discipline: to form knowledge with the current state of the theory of single-phase and multi-phase flows. The basics of classification of two-phase flows are presented. The strategy of building a generalized mathematical model of multiphase flows using the Eulerian and Lagrangian approaches is described. Models of specific problems of the dynamics of multiphase media with phase transitions are shown. Derivation of the equations of motion and energy of a heterogeneous medium with phase transitions. During the study of course, master students should be competent in: –deriving the basic equations of multiphase flow. –usingthe Eulerian approach to describe the movement of continuous media in different aggregative states; –usingthe Lagrangian method to describe the motion of continuous media that are in a different aggregative state; –to be able to model specific tasks of the dynamics of multiphase media. –deriving the equation of motion and energy of a heterogeneous medium with phase transitions. During the study of the discipline, master students will learn following aspects: Multiphase flows in nature and technology, features of mathematical and physical modeling of heterogeneous flows. The main characteristics of heterogeneous flows. Collision of particles between themselves. Stokes numbers. Classification of heterogeneous turbulent flows. Mathematical modeling of turbulent gas flows with particles. Lagrange approach: advantages and limitations. Eulerian approach: advantages and limitations. The strategy of building a generalized model of two-phase flows. Models of problems of the dynamics of multiphase media with phase transitions. Derivation of the equations of motion and energy of a heterogeneous medium with phase transitions.

Modeling of the Turbulent Flows

Type of control - [RK1+MT+RK2+Exam] (100)
Description - The purpose of the discipline is the formation of student’s knowledge about the methods of modeling turbulent flows. The problems of closure of Reynolds-averaged Navier – Stokes equations are described. The concepts of Reynolds stress and turbulent viscosity are given. The main models of turbulence will be shown, in particular, models with one equation for the energy balance of turbulence, two-parameter models, and models with the equations of transfer of components of the Reynolds stress tensor. During the study of course, master students should be competent in: –averaging over time and space the Navier-Stokes equations. –deriving the transfer equations of second-order point-like correlation moments. –understanding the basic of semi-empirical models of turbulence. –to be able to build models of turbulent viscosity and diffusion, models with one equation for the energy balance of turbulence. –to be able to build two-parameter models of turbulence. Models with differential equations for the transfer of components of the Reynolds stress tensor. During the study of the discipline students will learn following aspects: Reynolds-averaged equations of motion for a viscous compressible fluid. Equations for Reynolds stresses. The equation for the kinetic energy of turbulent pulsations. Equation for isotropic turbulence dissipation. Algebraic models of turbulence. Model of the Prandtl way of mixing. Single equation models. Equation for turbulent viscosity. Models with two differential equations. Dissipative two-parameter model of turbulence. Modeling the terms of generation, dissipation and diffusion in the equation for isotropic dissipation. Two-parameter k-ε model of turbulence, k-ω-Wilcox model.

Modeling the stability of a deformable systems

Monte-Carlo methods and their applications

Numerical methods for solution of the Navier-Stokes Equations

Type of control - [RK1+MT+RK2+Exam] (100)
Description - The purpose of the discipline: to form knowledge about the problems of the numerical solution of the Navier-Stokes equations. Methods for the numerical solution of the Navier-Stokes equations in the case of an incompressible fluid on a spaced grid will be shown. The methods for solution the variables in the function - vorticity parameters are shown. The solution methods for a viscous compressible fluid are studied, in particular, the McCormack method, the Bima-Warming method, the Godunov method, the TVD scheme During the study of course, master students should be competent in: – deriving the Navier-Stokes equations of a viscous compressible flow, to made dimensionless the parameters characterizing the motion of a viscous fluid. – creating a mathematical model of hydrodynamic processes, including the physical formulation of the problem, –formulating initial-boundary problems. – demonstrating knowledge of the basic finite difference, finite element and finite volume approaches to solving boundary value problems for the Navier-Stokes equations. – mading the program of the constructed numerical schemes for solving problems of hydrodynamics, to obtain results and to be able to interpret the mechanisms of the physical process. During the study of the discipline master students will learn following aspects: derivation of the Navier-Stokes equations, conservation laws, and basic hypotheses. Problems of numerical solution of equations. Numerical methods for solution of the Navier-Stokes equations in the case of incompressible fluid. The methods for solution the variables in the function - vorticity parameters are shown. Solutions for viscous compressible fluid, Mac-Cormac method, Bima-Warming method, Godunov method, TVD schemes, explicit implicit integration methods.

The turbulent flows, principles and applications

Type of control - [RK1+MT+RK2+Exam] (100)
Description - The purpose of the discipline: to form students' basic knowledge of the theory of turbulence and its principles. The concepts of turbulence are given, methods for describing the structures of turbulent flows are described. The basic principles of the Kolmogorov theory of developed homogeneous isotropic turbulence are given, in particular, concepts of the scale of turbulence, the spectrum of turbulent pulsations are given, the essence of the energy-containing and dissipative region of wave numbers. During the study of course, master students should be competent in: – understanding the processes of stability of a stationary fluid flow, the critical Reynolds number. –knowing the basic principles of the Kolmogorov phenomenological theory of developed homogeneous isotropic turbulence, – understanding the essence of the energy-containing and dissipative region of wave numbers. –deriving the Navier-Stokes equations for the motion of a viscous compressible fluid, to dimension the parameters that characterize the motion of a viscous fluid. – averaging the equations of a viscous fluid and deriving the Reynolds stress tensor. Understand closure problems of averaged equations. During the study of the discipline master students will learn following aspects: Fundamentalsof the theory of turbulence and its principles, concepts of turbulence, methods for describing the structures of turbulent flows. The main basics of Kolmogorov’s theory of developed homogeneous isotropic turbulence, the concepts of turbulence scales, the spectrum of turbulent pulsations. The essence of the energy-containing and dissipative region of wave numbers. The averaging of the equations of a viscous fluid and the derivation of the Reynolds stress tensor, the problem of the closure of averaged equations.

Theory of Generalized and Special Functions

Type of control - [RK1+MT+RK2+Exam] (100)
Description - The purpose of the discipline:to introduce students to the mathematical apparatus of the theory of generalized functions and various operations on them. Outlines the basics of the theory of generalized functions and operations on them. It also presents the basics of integral Fourier and Laplace transforms in the space of generalized functions and methods for constructing solutions of partial differential equations. During the study of course, master students should be competent in: – using the main types of special functions, their integral representations, asymptotics for solving problems of mathematical physics, – applying the theory of generalized functions to the solution of applied problems of mathematics and programming. – knowing the methodology of the study of functions, the rules of action in terms of calculating infinitely small quantities and the transition to integrated systems. – to be able to differentiate and integrate, investigate series and sequences for convergence, solve extremal problems, construct graphs of functions, solve equations and inequalities. – possessing the methods of formulation, analysis and solution of problems of differential and integral calculus, skills of independent solution of problems of theoretical and applied nature. During the study of the discipline master students will learn following aspects: Fundamentals of the theory of generalized functions and operations on them; fundamentals of integral Fourier and Laplace transforms in the space of generalized functions and methods for constructing solutions of partial differential equations. Generalized functions of one variable, operations with them. The main functions of many variables. The space of the main functions. Generalized functions of many variables, operations with them.

Data for 2021-2024 years

INTERNSHIPS

Pedagogical

Research

Data for 2021-2024 years