PhD courses
Speciality Code:
8D06104
Speciality Name:
Mathematical and Computer Modelling
Faculty:
Mechanics and Mathematics
Qualification:
- Scientific and pedagogical direction - Doctor of Philosophy (PhD)
- Model of graduating student
- Mandatory disciplines
- Elective disciplines
- Professional
ON1. Conduct scientific research and obtain new fundamental and applied results, plan scientific and analytical research in accordance with the approved direction of research in the field of specialization.
ON2. Use the concepts, mechanisms and patterns of physical, chemical and technological, natural, biological and random processes when developing conceptual and theoretical models of scientific problems solved.
ON3. Use multiprocessor computing techniques and methods of mathematical, numerical and computer modeling during the analysis and solution of applied and engineering problems, exposing the use of skills to expand their knowledge based on information and educational technologies.
ON4. Create a project and develop recommendations for the implementation of research results in the production and financial industries by methods of mathematical modeling and numerical experiments.
ON5. Carry out an in-depth analysis of the problems, statement and justification of the problems, reveal their natural and scientific content during scientific and research activities, involve the corresponding mathematical apparatus for their solution.
ON6. create mathematical and computer models to solve the problems of biomedical processes, processes of physical chemistry, kinetics, financial processes, dynamics of multiphase turbulent flows.
ON7. Analyze, develop and conduct numerical experiments of constructed mathematical models of industrial, technological, non-stationary physical, chemical, biological, financial processes.
ON8. Develop stochastic finance models; choose approximate methods to model turbulence and techniques for closing the governing equations using a semi-empirical theory.
ON9. Conduct scientific research in the field of mathematical and computer modeling of temperature phenomena, complex systems, thermomechanical processes, as well as apply stochastic and simulation systems to solve research and applied problems.
ON10. Conduct research and experiments to apply mathematical and numerical tools of fundamental knowledge on numerical methods, financial mathematics, computational fluid dynamics, mechanics, turbulence modeling, physical, biomedical, and nonlinear technological processes and complex systems for solving applied problems.
ON11. Develop educational materials, educational and methodical complexes of disciplines in the field of mathematical and computer modeling, modern numerical methods; develop and introduce new innovative education technologies to pedagogical practice.
ON12. Carry out research with foreign partners in order to prepare results for the implementation of interstate programs in the field of mathematical modeling, mathematics and mechanics; participate in scientific seminars and conferences, maintain international communication with scientific community; work as a team, tolerate social, ethnic, religious and cultural differences, critically evaluate individual and team activities, identify ways and choose the means for self-development and enhancing skills.
ON2. Use the concepts, mechanisms and patterns of physical, chemical and technological, natural, biological and random processes when developing conceptual and theoretical models of scientific problems solved.
ON3. Use multiprocessor computing techniques and methods of mathematical, numerical and computer modeling during the analysis and solution of applied and engineering problems, exposing the use of skills to expand their knowledge based on information and educational technologies.
ON4. Create a project and develop recommendations for the implementation of research results in the production and financial industries by methods of mathematical modeling and numerical experiments.
ON5. Carry out an in-depth analysis of the problems, statement and justification of the problems, reveal their natural and scientific content during scientific and research activities, involve the corresponding mathematical apparatus for their solution.
ON6. create mathematical and computer models to solve the problems of biomedical processes, processes of physical chemistry, kinetics, financial processes, dynamics of multiphase turbulent flows.
ON7. Analyze, develop and conduct numerical experiments of constructed mathematical models of industrial, technological, non-stationary physical, chemical, biological, financial processes.
ON8. Develop stochastic finance models; choose approximate methods to model turbulence and techniques for closing the governing equations using a semi-empirical theory.
ON9. Conduct scientific research in the field of mathematical and computer modeling of temperature phenomena, complex systems, thermomechanical processes, as well as apply stochastic and simulation systems to solve research and applied problems.
ON10. Conduct research and experiments to apply mathematical and numerical tools of fundamental knowledge on numerical methods, financial mathematics, computational fluid dynamics, mechanics, turbulence modeling, physical, biomedical, and nonlinear technological processes and complex systems for solving applied problems.
ON11. Develop educational materials, educational and methodical complexes of disciplines in the field of mathematical and computer modeling, modern numerical methods; develop and introduce new innovative education technologies to pedagogical practice.
ON12. Carry out research with foreign partners in order to prepare results for the implementation of interstate programs in the field of mathematical modeling, mathematics and mechanics; participate in scientific seminars and conferences, maintain international communication with scientific community; work as a team, tolerate social, ethnic, religious and cultural differences, critically evaluate individual and team activities, identify ways and choose the means for self-development and enhancing skills.
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History and Philosophy of Science
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose: Understanding of modern philosophy as a system of scientific knowledge, including worldview in rational-theoretical comprehension. The discipline includes aspects of the evolution and development of scientific thinking, historical moments, the contribution of scientists and scientific schools to the formation of science, and ethical and social aspects of scientific activity.
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Scientific Research methods
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of studying the discipline "Research Methods " is to develop the ability of doctoral students to conduct research based on the analysis, systematization and generalization of research results in the field of mathematical and computer modeling through the use of a set of research methods for solving specific applied problems . As a result of studying the discipline, doctoral students will be able to: 1. to abstract thinking, analysis, synthesis, the ability to improve and develop their intellectual and General cultural level; 2. to master and use new research methods in a new field of professional and research activities; 3. to use knowledge of modern problems of science and education in solving fundamental and applied problems; 4. to analyze the results of scientific research, apply them in solving specific applied problems, independently carry out scientific research; 5. to use individual creative abilities to independently solve research problems; 6. to carry out scientific research, create innovations, implement them in reality, analyze and reflect the results. During the study of the discipline students will learn following aspects: methodologies, methods, problems, principles, and trends that are necessary for specialists in mathematical and computer modeling to develop and implement scientific research and research projects to improve the efficiency of organizations, industries, and regions in various areas of the economy. This course introduces the categories and basic concepts of research methodology, forms and methods of scientific knowledge, principles and organization of research activities; the main problems of modern research practice, teaches to use various information resources, introduces the methodology of writing, registration and defense of dissertation work.
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Academic writing
- Number of credits: 2
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of studying the discipline "Academic writing" is to develop PhD doctoral students' respective professional competencies aimed at developing the willingness and ability of scientific and pedagogical personnel to implement their own research projects, programs, and presenting their results in writing in accordance with the legislative norms of the Republic of Kazakhstan and international academic community, the ability to show publication activity in national and foreign language. As a result of studying the discipline, doctoral students will be able to: 1. Formulate productive research questions; to formulate the goal, objectives, subject and object of scientific work; prepare a description of the research in Kazakh, Russian or Englishlanguage in order to publish the results in a highly rated journal. 2. To navigate in the literature on the topic of research, use bibliographic resources and search engines for scientific work, including electronic databases; 3. Reasonably state the provisions of their study, based on facts and examples. 4. Prepare and submit documents for obtaining a patent and copyright . 5. Substantially conduct a discussion on the topic of research in order to disclose a research question and develop methodological tools for the implementation of a scientific project. Implement a scientific project in accordance with the requirements of competitive documentation or as part of initial research. 6. Write a review of a scientific project / article / dissertation.During the study of the discipline students will learn following aspects: the main aspects of compiling academic texts in Kazakh, Russian and English are considered in order to publish the results of scientific research in the form of dissertations, scientific articles or project applications. We study the features of writing project applications for tender documentation for funding of scientific research; patent applications and applications for obtaining copyright. This course includes the study of the main aspects for the formulation of goals, objectives, relevance of research, etc. Students will learn how to carry out comprehensive research, including interdisciplinary, on the basis of a holistic systemic scientific worldview, to learn how to describe the research work done in Kazakh, Russian and English.
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Mathematical modeling of nonstationary physical processes
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: to form the ability to simulate non-stationary physical processes using mathematical methods. During the study of course, students should be competent in: - describing the finite-difference methods for the approximate solution of the equations of mathematical physics; - selecting a mathematical model for the physical problem in the form of multi-dimensional time-dependent differential equations; - creating numerical algorithms and programs for the implementation on PC; - analyzing the results, their physical meaning; - assessing the accuracy of computations. During the study of the discipline students will learn following aspects: the construction of a mathematical model of the physical process; the correct choice of the mathematical model and the numerical method; construction of difference schemes and algorithms for solving problems; construction of flowcharts and software code; analysis of the results of numerical simulation of problems of nonlinear physical processes.
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PhD thesis writing and defence
- Number of credits: 12
- Type of control: Докторская диссертация
- Description: The main purpose of "PhD thesis writing and defence": of a doctoral dissertation is the formation of the doctoral students' ability to disclose the content of research work for the defense of the thesis. During the study of course, doctoral student's should be competent in: 1. to substantiate the content of new scientifically grounded theoretical and experimental results that allow to solve a theoretical or applied problem or are a major achievement in the development of specific scientific directions; 2. explain the assessment of the completeness of the solutions to the tasks assigned, according to the specifics of the professional sphere of activity; 3. they can analyze alternative solutions for solving research and practical problems and assess the prospects for implementing these options; 4. apply the skills of writing scientific texts and presenting them in the form of scientific publications and presentations. 5. to plan and structure the scientific search, clearly highlight the research problem, develop a plan / program and methods for its study, formalize, in accordance with the requirements of the State Educational Establishment, the scientific and qualification work in the form of a thesis for a scientific degree Doctor of Doctor of Philosophy (PhD) on specialty «8D07502 – Standardization and certification (by industry)». During the study of the discipline doctoral student will learn following aspects: Registration of documents for presentation of the thesis for defense. Information card of the dissertation and registration-registration card (in the format Visio 2003). Extract from the minutes of the meeting of the institution, in which the preliminary defense of the thesis took place. Cover letter to the Higher Attestation Commission. Expert conclusion on the possibility of publishing the author's abstract. Expert opinion on the possibility of publishing a dissertation. Minutes of the meeting of the counting commission. Bulletin for voting. A shorthand record of the meeting of the dissertational council. List of scientific papers. Response of the official opponent. A review of the leading organization. The recall of the scientific adviser.
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Mathematical and computer modeling of medical and biological processes
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline: to form knowledge in solving actual scientific and applied problems related to modeling processes occurring in living organisms and systems, processing and system analysis of experimental data, to form knowledge in the field of the theory of dynamic systems and nonlinear dynamics applied to the problems of physics of living systems.
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Psychology of management
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Formation of knowledge about the fundamental concepts of management psychology for the practical application of the most critical aspects of management in professional interaction. Basic principles of management psychology, personality in management interactions, management of personality behavior, modern ideas, psychology of managing group phenomena, motivation, and practical reflection.
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Modern methods of mathematical modeling
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline: to form the skills of applying theoretical and practical aspects of modern modeling methods for solving problems of applied mathematics, skills of using mathematics packages corresponding to tasks, to form skills to interconnect modules implemented in math packages with software implemented using high-level programming languages (Python, Java). Modern mathematical packages will be studied that allow solving applied problems of natural science.
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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.
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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.
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Simulation Modeling of Complex Systems
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: to form the ability to create simulation models for solving applied and research problems based on various modern platforms. During the study of the course, students should be competent in: - demonstrating fundamental, systemic knowledge in the field of simulation modeling of applied and research problems; - conducting critical analysis, evaluation and synthesis of new and complex ideas, problems, approaches and trends in the application of simulation systems; applying general programming knowledge in application development; - generating new and complex goals, proposing new hypotheses and solutions of scientific problems in the field of principles for constructing simulation models of systems and processes of their functioning; - applying the methods of system dynamics and discrete event modeling for the development of simulation models; - working skills in the instrumental environment of simulation modeling using the means of visual development of the model; - differentiating the priorities of educational and research activities, correlating their own scientific interests with social, ethnic values, the needs of production and society; - presenting the results of educational and research activities in the form of scientific reports, abstracts, abstracts of articles, physical and mathematical comments, doctoral dissertations, educational research and scientific projects. During the study of the discipline, students will learn the following aspects: Development of simulation models of processes and systems, development of decision support systems, automation of production processes. Software design. Designing user interfaces. Confidentiality and ethical standards. Ergonomics and accessibility. Project management.
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Computer modeling in dynamic systems
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: to form the knowledge in the field of the theory of dynamical systems and nonlinear dynamics as applied to the problems of the physics of living systems; ability to solve applied problems; know the methods of identification of dynamic systems and decision making. During the study of course, students should be competent in: - describing: the main provisions of the qualitative theory of differential equations, the terms and approaches of the theory of dynamic systems; - solving theoretical problems of system analysis and systems theory, - formulating the tasks of analytical and numerical research of dynamic systems on the phase plane and in the three-dimensional phase space and choose adequate theoretical and numerical methods for their solution. - possessing an analytical method for analyzing the stability of equilibrium states of models of living systems, to own computer methods for analyzing stability in the phase space of a model system. - solving research and applied problems. During the study of the discipline, students will learn following aspects: concept of a dynamic system, linear and nonlinear dynamical systems, existence and uniqueness of the solution, phase space, phase trajectory and semi trajectory, singular points, search and analysis of the stability of equilibrium states in two-dimensional and three-dimensional systems, determination of the equilibrium state in living systems, elements of bifurcation theory, structural stability and bifurcation.
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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.
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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.
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Computer modeling of complex system using Python
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: to form the ability to create complex computer models based on the Python platform. During the study of the course, students should be competent in: - demonstrating fundamental, systemic knowledge in the development of computer modeling of complex systems within the framework of modern scientific knowledge paradigms; - conducting a critical analysis, evaluation and synthesis of new, complex ideas, problems, approaches and trends in determining specific requirements in developing a computer model; - working with the test results and processing the experimental results with the methods of mathematical processing of experimental data; - critically evaluating the results of scientific research, modern theories, problems and approaches, new trends in the study of the model and the obtained modeling data; - differentiating the priorities of educational and research activities, correlating their own scientific interests with social, ethnic values, the needs of production and society; - presenting the results of educational and research activities in the form of scientific reports, abstracts, abstracts of articles, physical and mathematical comments, doctoral dissertations, educational research and scientific projects; - conducting independent research of scientific problems with a projection on promising new directions in computer modeling of complex systems using Python. During the study of the discipline, students will learn the following aspects: Computer simulation of complex thermo-physical processes. Python programming language. Python-based software design. Designing user interfaces. Confidentiality and ethical standards. Ergonomics and accessibility.
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Mathematical Models for Heat and Mass Transfer problems
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: to form the ability to apply a generalized method for calculating the heat and mass transfer of fluid flows and related processes; to compose an algorithm for the numerical solution of the problem, the implementation program on PC; to analyze the results, their physical meaning; to evaluate the error of calculations. During the study of the course, students should be competent in: - choosing a computational method for solving problems; - constructing numerical algorithms; - making the program for implementation on PC; - analyzing the results, their physical meaning; - assessing the accuracy of computations. During the study of the discipline, students will learn following aspects: main aspects of mathematical modeling of heat and mass transfer in electrical contacts, various methods of implementation on a PC.
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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.
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Mathematical models of two-phase process control
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: to form the ability to build a generalized computer model of multiphase flows. During the study of the course, students should be competent in: - independently simulating multiphase turbulent flows; - using multiphase flow equations for solving practical problems; - using the primary characteristics of multiphase flows for their classification; - obtaining a general idea of the methods for calculating the characteristics of two-phase turbulent flows; - mastering information about the transfer processes in single-phase and multiphase turbulent flows. During the study of the discipline, students will learn the following aspects: the current state of the theory of single-phase, multi-phase flows; transport processes in single-phase and multiphase turbulent flows; methods for calculating the characteristics of two-phase turbulent flows; classification of two-phase turbulent flows; primary characteristics of multiphase flows for their classification and modeling.
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Mathematical and computer modeling of temperature phenomena
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: to form the ability to develop a computer-aided mathematical model of a steady-state temperature field in structural elements with simultaneous presence of heterogeneous local heat sources. During the study of the course, students should be competent in: - identifying specific requirements, opportunities and problems in the development of a mathematical model of temperature phenomena; - systematizing and interpreting scientific theories and concepts of the latest trends in mathematical and computer modeling; - applying 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 and temperature phenomena; - differentiating the priorities of educational and research activities, correlating their own scientific interests with social, ethnic values, the needs of production and society; - presenting the results of educational and research activities in the form of scientific reports, abstracts, abstracts of articles, physical and mathematical comments, doctoral dissertations, educational research and scientific projects; - building a research process on the topic of the thesis, reasonably submit the research results in scientific discussions and publications in rating journals in international databases of Thomson Reuters or Scopus, as well as in national and international peer-reviewed publications. During the study of the discipline, students will learn the following aspects: Modeling of complex thermo-physical processes and temperature phenomena. Programming languages. Software design. Designing user interfaces. Confidentiality and ethical standards. Ergonomics and accessibility. Principles and methods of applying the fundamental laws of energy conservation in the study of temperature phenomena in the bearing elements of the structure, taking into account the simultaneous presence of local dissimilar heat sources.
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Mathematical modeling in Biomedical Engineering
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: to form the ability to state the problems of mathematical modeling of biomedical processes, taking into account the characteristics of biological objects, methods of assessing their properties; to classify models by their properties, specificity of the object; to develop models, choose the research methods; to carry out a meaningful interpretation of the modeling results. During the study of course, students should be competent in: - analyzing the complex, incomplete or contradictory areas of knowledge, effectively conveying the results. - synthesizing information on processes, occurring inside the human body. - critical evaluating the research, advanced scholarships and methodologies and arguing alternative approaches. - demonstrating initiative and originality in solving problems. - acting autonomously when planning and executing tasks at the professional or equivalent level, making decisions in complex and unpredictable situations. The objectives of the course is to develop a deep and systematic understanding of the problems of transport processes in the human body, the ability to compile mathematical models for complex processes in this field of knowledge, to implement them, selecting a numerical method, and the ability to analyze the results obtained. During the study of the discipline, students will learn the following aspects: basic concepts of biomedical engineering; mathematical models of complex processes in this area; classification of mathematical methods.
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Turbulence modeling techniques (RANS)
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: to form the ability of doctoral students to choose the right approximate methods of modeling turbulence based on the Reynolds method. During the study of the course, students should be competent in: - quantitatively analyzing the obtained numerical results; having a clear idea of the algorithm for solving problems; - selecting and justifying the methods chosen; having the culture of thinking; understanding the importance and the main problems of the discipline; - closing the system of equations for the averaged values; - building a numerical algorithm for solving differential equations; - writing the code, analyzing the results of numerical simulation of turbulent flows. The objective of the discipline is oriented the doctoral correct choice of approximate methods for solving problems. Since the module as a whole is focused on methods for solving nonlinear partial differential equations, which are characterized by discontinuous solutions (for hyperbolic type equations), large gradient domains (“boundary layers”), etc., a lot of attention is paid to building monotone (majorant) schemes. During the transition from model equations to linear systems and nonlinear equations, the course actively uses the characteristic properties of hyperbolic type equations and similar splitting methods for other types of equations, the integral-interpolation method (integral identity method) and other effective ways of generalizing schemes with preserving properties. During the study of the discipline students will learn the following aspects: semi-empirical theory of turbulence, the characteristic properties of statistical moments of higher order, obtained on the basis of equations for Reynolds stresses; one-parameter, two-parameter models of turbulence; building semi-empirical models for Reynolds stresses in the field of external forces.
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Methods of parametrization in the statistical dynamics of turbulence
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: to form the ability to build models of turbulence taking into account the influence of external forces. During the study of the course, students should be competent in: - the ability to close the equations of motion in various environments under the action of external forces; -the ability to build models of the circuit, taking into account the influence of external forces, with all the forces parameterized relative to the inertia force; -the ability of the constructed models of turbulence, depending only on the local parameters of the turbulent flow; - solving problems of turbulence in stratified media; - solving problems in the field of magnetic forces; in the field of double external forces. During the study of the discipline, students will learn the fol0lowing aspects: Methods of closure of the equations of motion in various media under the action of external forces will be studied. The closure models will take into account the influence of external forces, with all forces parameterized relative to the inertia force. The constructed models of turbulence will depend only on the local parameters of the turbulent flow. In studying the discipline, students will study the following aspects: a semi-empirical theory of turbulence, the characteristic properties of statistical moments of higher order, derived from the equations for Reynolds stresses; construction of parametrized statistical models for Reynolds stresses in the field of external forces.
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Modeling of nonlinear deformable systems and processes
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: forming the ability of doctoral students to obtain the basic relations and characteristics of nonlinear deformable media for their practical application while modeling of applied problems of the elasticity theory. During the study of course, students should be competent in: - demonstrating a deep understanding and ability to develop mathematical models of nonlinear deformable systems and processes; - understanding and explaining the basic principles underlying the nonlinear mathematical models of deformable systems and processes; - properly applying the methodological apparatus of the nonlinear theory of deformable media to solve nonlinear mathematical models; - critically analyzing and evaluating the results of modeling of nonlinear deformable systems and processes; - integrating knowledge on modeling of nonlinear deformable systems and processes to solve important applied problems and determining the significance of products of their own and other scientific activities. During the study of the discipline students will learn the following aspects: concept of deformation functional; construction of the functional of elastic deformation for a nonlinear medium at various approximations; variation principles; application of variation principles for the development of nonlinear mathematical models; selection of methods and finding solutions to models of nonlinear applied problems; visualization of the research results.
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Modeling of financial risks
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: TThe purpose of the discipline: on the example of an insurance company, give the following basic concepts: Uncertainty. Risk. Risk portfolio. Insurance. Insurance portfolios. The simplest insurance portfolio. Simple insurance portfolio. Real insurance portfolio. Pricing principles and quantification of risk aversion. Classical and aggregate risk processes. Process ruin and lifetime of risk processes. In the course of studying the course, to form students' abilities: During the study of course, master students’ should be competent in: -determine the features of modeling classical and aggregated financial risk processes; - to implement the compiled mathematical models; - demonstrate and apply in practice the main methods of modeling financial risks; - apply the mathematical apparatus and check the adequacy of the models; - analyze the simulation results. During the study of the discipline, students will learn following aspects: using the systems of concepts used to describe financial risk models, study their occurrence and calculate quantitative expressions; use of modern mathematical models and methods in the field of financial random processes; features of modeling financial stochastic risk processes, basic methods of statistical analysis; methods of research of the insurance and financial markets.
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Mathematical and computer modeling of physical chemistry processes
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: to form the ability to develop a mathematical model for the problem of physical chemistry; algorithm and program for the numerical solution of the problem; to analyze the results, their physical meaning; to estimate the computation error. During the study of the course, students should be competent in: - selecting a mathematical model for the problem of physical chemistry in the form of differential equations of mathematical physics; - creating the numerical algorithm, the program for implementation on PC; - analyzing the results, their physical meaning; assessing the accuracy of calculations. - describing the various problems of physical chemistry and mathematical models; - applying numerical methods for solving equations of mathematical physics describing physical problems. During the study of the discipline, students will learn the following aspects: basic principles of construction and verification of mathematical models of biological systems: enzymatic reactions, metabolic and signaling pathways, pathways of cellular dynamics, physical chemistry processes; finite difference methods for approximate solution of the models obtained, various modeling methods for solving problems of biomedicine and pharmacology.
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Turbulence modeling: LES-approach
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: to form the ability to simulate the statistical parameters of turbulent flows, their non-stationary vortex structure; choose a turbulence model for solving a specific problem using CFD packages. During the study of the course, students should be competent in: - describing the concepts of the theory of turbulence, its hypotheses and the main consequences; - applying the method of large eddies, learning the concepts of spatial filters and sub grid stresses; - understanding the LES filtered Navier-Stokes equations; - mastering the basic methods of closure of these equations to create semi-empirical models; - choosing a model of turbulence to solve a specific problem, including the use of CFD packages. During the study of the discipline, students will learn the following aspects: the theory of turbulence, hypotheses and main consequences; large eddy method; concepts of spatial filters, sub grid stresses; the main methods of closure of LES filtered Navier-Stokes equations for creating semi-empirical models.
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Methods in inverse-problem and optimization
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: to form the ability of doctoral students to carry out the formulation of the problem, to select the method of solution; to analyze the results obtained, to prove it; to apply basic methods for solving inverse problems. During the study of the course, students should be competent in: - knowing the basic optimization methods for solving inverse problems; - being able to formulate the problem, to select the method of solution; - making an algorithm for the numerical solution of the problem, a program for implementation on a PC and carry out feedback; - being able to analyze the results obtained, their physical meaning; - estimate the error of calculations. During the study of the discipline, students will learn the following aspects: Conception of Inverse Problem. Inverse Problems for Two-Dimensional Parabolic and Elliptic Equations. The Connection between Inverse Problems for Parabolic, Elliptic and Hyperbolic Equations. Numerical Solution of Inverse Problems for Parabolic, Elliptic and Hyperbolic Equations. Boundary Inverse Problem for Parabolic Equation. Statement of Problem. Optimization Method of Solution. Functional of Solution. Principle of Maximum for Boundary Inverse Problem for Parabolic Equation. Adjoint Problem. Numerical Algorithm of Solution. Method of Quickest Descent. Iterative Method.
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Physical nonlinearity in problems of dynamics
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: forming the ability of PhD students to model physically nonlinear media and apply them while solving applied problems. During the study of course, students should be competent in: - demonstrating a systematic understanding of scientific information in the field of modeling physically nonlinear media, knowledge and studying new research methods in the subject area; - classifying physically nonlinear problems, boundary conditions, external and internal forces; - conducting the comparative analysis, evaluation and reasoned choice of elastic potentials of physically nonlinear media; - applying the methodological apparatus of the nonlinear theory of deformable media to solve physically nonlinear mathematical models; - critically analyzing and evaluating the modeling results of physically nonlinear deformable media; - highlighting applied aspects while modeling nonlinear problems of deformable media and integrating the knowledge gained; - creating a holistic scientific work and determining the significance of products of own and other scientific activities During the study of the discipline students will learn following aspects: elastic potentials; selection of elastic potentials for the description of physically nonlinear media; construction of basic relations and state equations; determination of methods for solving physically nonlinear models; use of application software packages for solvingthe problems and visualizing the results obtained.
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Numerical methods in chemical kinetics
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: to form the ability to master the principles of mathematical modeling of complex chemical processes. During the study of the course, students should be competent in: - analyzing complex information, managing the complexity, inadequacy of data or contradictions in the field of numerical methods in chemical kinetics; - synthesizing new approaches that promote the development or understanding of the methodology in quantitative methods in chemical kinetics; - having a conceptual understanding and critical capabilities that allow independent evaluation of research, advanced technologies and methodologies; - arguing alternative approaches; - managing planning and execution of the problems on a professional or alternative level and independently responding to problem solving. During the study of the discipline, students will learn the following aspects: main types of chemical problems; numerical methods for solving and integrating systems of differential equations; the basis of the mechanisms of chemical reactions occurring in the given system; changes in the quantitative characteristics of chemical reactions over time and the effect of the parameters of the reaction system on the rate of conversion.
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Random processes and financial mathematics
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: to form the ability to identify and highlight key materials, develop mathematical models, create financial models, apply them to solve tasks and analyze the results obtained. During the study of the course, students should be competent in: - identifying and highlighting the key materials; - developing mathematical models; - applying to solve tasks; - analyzing the results; - creating and prepare financial models. During the study of the discipline, students will learn following aspects: concepts, structures, tools, goals and objectives of financial theory and financial engineering. Random processes. Stochastic models. Statistical analysis of financial data.
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Stochastic models and the theory of calculations in stochastic financial models
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: to form the knowledge on the main stochastic models: linear, non-linear stochastic conditional Gaussian, non-Gaussian, Brownian-based models, diffusion models; ability to perform calculations in stochastic financial models. During the study of the course, students should be competent in: - identifying and highlighting the key materials; - developing mathematical models; - solving the tasks; - analyzing the results; - offering the models. During the study of the discipline, students will learn following aspects: The main stochastic models: linear, nonlinear stochastic conditional Gaussian, non-Gaussian, Brownian-based models, diffusion models. Theory of calculations in stochastic financial models. Options of American and European types.
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Numerical simulation of unsteady three-dimensional turbulence flows
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: to form the ability to conduct numerical simulation of unsteady three-dimensional turbulent flows; to compile an analysis of the results, to organize a computational experiment. During the study of the course, students should be competent in: - describing a variety of physical processes and mathematical models; - applying numerical methods to solve equations of mathematical physics describing physical problems; - describing the issues of convergence, stability of the applied schemes and algorithms, computation errors; - conducting numerical simulation of unsteady three-dimensional turbulent flows, selecting the method for solving the problem, and also compiling an analysis of the results obtained. - organizing a computational experiment. During the study of the discipline, students will learn the following aspects: various physical processes and mathematical models for describing turbulence problems and calculation methods; development and implementation of models of turbulence from the simplest semi-empirical models to modern direct methods.
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Numerical methods of high order accuracy
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: to form the ability to build grid schemes by the finite difference method, finite volume method for the aerodynamics and heat transfer problems; to simulate thermodynamic processes, to develop computer-aided calculation programs, to correctly analyze the results of calculations. During the study of the course, students should be competent in: - describing the formulations of the basic fundamental physical laws and their main consequences in relation to the problems of aerodynamics, the basic numerical approaches, methods and algorithms for the implementation of models of thermal processes; - studying grid circuits by the finite difference method, finite volume method for typical problems of aerodynamics and heat transfer; - conducting numerical solution of discontinuous problems by various methods and correctly analyze the results of calculations; - applying methods for constructing finite difference, finite volume grids; - developing a software systems for computing on a computer based on the constructed numerical methods for solving problems of aerodynamics computer. During the study of the discipline, students will learn following aspects: hyperbolic systems of conservation laws and problems of their solution; cross-counting schemes, explicit and implicit methods for solving initial equations; TVD schemes (monotonous reconstruction, slope limiters). High order methods. ENO and WENO; methods for constructing finite-difference, finite-volume grids.
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Nonlinear Theory of Deformable Media
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main purpose of the course: forming the doctoral knowledge on the theory of nonlinear deformable media for practical application while modeling processes and phenomena at the new qualitative level. During the study of the course, students should be competent in: - demonstrating a deep understanding and ability to apply the conceptual apparatus of the V.V. Novozhilov nonlinear theory of deformable media; - competently operating with the basic equations of the nonlinear theory of deformable media; - classifying nonlinear problems, boundary conditions, external and internal forces; - conducting a critical analysis of the strain-stress state of various deformable media in nonlinear formulation; - creating a holistic scientific work using the basic relations, principles and methods of the V.V. Novozhilov nonlinear theory. During the study of the discipline students will learn following aspects: fundamentals of the V.V. Novozhilov nonlinear theory, strain-stress state of the medium in nonlinear formulation; basic assumptions of the nonlinear theory; equations of media and boundary conditions; physical meaning of the V.V. Novozhilov simplifications; application of the nonlinear theory for modeling of various processes and phenomena.
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Mathematical and Computer Modeling of Unsteady Nonlinear Physical Processes
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline: to develop skills for solving problems of studying non-stationary nonlinear physical processes by mathematical methods. In the course of studying the course, to form the abilities of undergraduates: – to make mathematical models of complex non-stationary nonlinear physical processes; – use numerical methods for the implementation of mathematical models of non-stationary nonlinear physical processes; - write a program code for the constructed mathematical model; – build a graph and analyze the results.
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Pedagogical
- Type of control: Защита практики
- Description: Aim оf discipline: formation of the ability to carry out educational activities in universities, to design the educational process and conduct certain types of training sessions using innovative educational technologies.
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Research
- Type of control: Защита практики
- Description: The purpose of the practice: gaining experience in the study of an actual scientific problem, expand the professional knowledge gained in the learning process, and developing practical skills for conducting independent scientific work. The practice is aimed at developing the skills of research, analysis and application of economic knowledge.