Module-6. Mathematical Modeling
IMM3301
Introduction to Mathematical Modeling
2 credits/
Pre: DU 2307, MA 1301, MA 1303
1+0+1
Mathematical modeling of real processes is one of the modern
and efficient methods for solving problems of scientific and
technological progresses. The basic of methodology of
mathematical modeling is the creation of an adequate
mathematical image of the object and its analysis by
computing and computer technology. Discipline is designed to
teach students the modeling of objects and phenomena of
different nature. This modeling of phenomena and processes
from different areas of science (mechanics, physics, biology,
chemistry, etc.) as well as modeling of ecological environment,
the financial and economic processes, and other hard objects
formalized. The course material contains a large number of
examples from various areas of human activity, which will
expand the horizons of the student as a researcher and will
provide skills in mathematical modeling.
skills, knowledge of mathematical modeling of
objects and their methods of selecting solutions
(theoretical or numerical analysis on a PC.)
-the ability to choose the criteria for mathematical
modeling of scientific and engineering problems, to
draw an analogy with the objectives of the other areas
of science
MCMBPhM4302
Mathematical
and
computer
modeling
in
biophysics and medicine
2 credits/
Pre: DU 2307, MA 1301, MA 1303
1+0+1
The use of mathematics in attempts to formulate the laws of
biology has a long history. But only now become possible an
integrated approach to all areas of biology and medicine. The
appearance of high-speed computers influenced to the research
in all areas of scientific knowledge. By modeling the various
processes of biology and medicine can study the influence of
various factors on these processes. The use of computer
technology for the diagnosis has not a few important.
-Knowledge of the universal properties of biomedical
systems and methods for their simulation;
-Ability to analyze mathematical models of
biomedical processes using mathematical methods
and computers;
MCMPhP4303
Mathematical and computer modeling of physical
processes
3 credits/
Pre: DU 2307, MA 1301, MA 1303
2+1+0
Course objective: This discipline is designed for bachelors who
want to acquire knowledge and skills to conduct research in the
field of modeling and simulation of physical processes.
Objectives of the course:
1) Drafting of mathematical models of complex physical
processes.
2) Techniques and methods to solve difficult problems in
mathematical physics.
3) Use a different numerical methods for physical processes.
4) to develop design skills, problem-and student-centered
learning in the course "Fundamentals of mathematical and
computer modeling of natural physical processes";
5) to develop skills of analysis and the development of pilot
research projects on the course;
Know the differential equations, the equations of
mathematical
physics,
numerical
methods,
programming languages C / C + + or Fortran,
mathematical analysis, fundamentals of mathematical
modeling
Be able to choose and use of information technology
for applications, the ability to operate a computer and
use the programming language
Be skilled in the construction of mathematical models
of physical processes, sampling differential equations
of mathematical physics, choose the correct
numerical
method,
write
code
to
construct
mathematical models, graphs and animations to
results
Module-7. Administration and Programming
Pro1301
Programming
3 credits/
Pre: MA 1301, MA 1303
1+0+2
The course provides an overview of the evolution of
programming languages. The notion of programming
environments, the basic structures of programming languages.
We consider high-level syntax and semantics of programming
languages including C + + and FORTRAN. The notion of
recursion,
recursive
mathematical
functions,
provides
examples of recursive procedures. Describes the basic data
structures and an analysis of their implementation in different
programming languages. Determined the simple types, arrays,
records, and structure. We consider the static and dynamic
memory management, placement in memory different data
types.
-Knowledge of the basic methods of effective
programming
-ability to implement numerical methods in a
procedural style.
Be skilled in procedural programming, programming
skills of high numerical methods, the use of effective
library of numerical methods, the use of popular
compilers on different operating systems.
SAOS2302
System Administration operating systems
3 credits/
Pre: Pro 1305, IT 1103
1+0+2
A typical UNIX-system has long been in the computer world a
few isolated niche. Despite the existence in standard bundle a
number of useful administrative tools, not all suppliers of
systems to adequately provide them with technical support. In
addition, many organizations receive significant amounts of
software from the university, on Usenet and other sources not
providing any support at all. System administrators -
employees whose duties include not only the tracking of
network security organization, but also to create the optimum
performance of computers and software to users, often linked
to the overall work of a certain result. This course is designed
to use the operating system Linux - the most common
operating systems. It can be considered and in relation to other
UNIX-like operating systems.
-Knowledge of the basic concepts of operating
systems Linux; knowledge of basic administration
tasks, knowledge of the initial stages of loading;
knowledge to stop and restart the system, about the
features of the file system operating system Linux, for
connecting new users, delete users, disabling the
account of the sequential access devices, for network
protocols TCP / IP, the procedure for adding a hard
disk
OOPC2303
Object-oriented programming in C++
3 credits/
Pre: Pro 1305
1+0+2
The programming language C - is a universal programming
language that allows you to develop programs in accordance
with different paradigms: procedural programming, object-
oriented parametric. This course covers all the main features of
the C language and its application in the development of
object-oriented programs. Brief description of library language
C, an overview of the fundamental concepts of the theory of
object-oriented programming with the features of the
programming language C (typing, inheritance, encapsulation,
polymorphism, dynamic binding, etc.).
- Basic knowledge of methods for efficient
programming in C + +.
-ability to implement numerical methods in C + + in a
procedural style.
Be skilled in procedural programming, programming
skills of high numerical methods, the use of effective
library of numerical methods, the use of popular
compilers on different operating systems.
PP2304
Parallel Programming
3 credits/
Pre: Pro 1305
2+0+1
The study of the basic technologies of parallel programming in
Open MP, skills and abilities for configuring cluster computing
operating systems, Linux, Windows. Debugging software,
application of the basic functions of Open MP for solving
complex problems of mathematical physics using the
programming languages C + + and Fortran 90.
To learn the most popular engineering of parallel
programming, the skills of programming on cluster
systems, debugging of parallel code.
Module-8 Computer graphics and databases
3DM3301
3D-modeling
3 credits/
Pre: Pro 1305
1+0+2
3ds Max - a system of three-dimensional modeling, rendering
and animation developed by Autodesk. With the help of 3ds
Max, you can create three-dimensional models of real objects,
to obtain photorealistic rendered image quality and create a
computer animation. This course is continuation of the course
3D-modeling, studied in a bachelor degree. The course
considers the physical processes modeling real-world modeling
and animation of models of living creatures using inverse
kinematics, simulation and animation of hair and wool,
modeling and animation of natural phenomena using particle
systems, the use of space probes and simulated the effects of
the environment, creating effects, editing, and familiarity with
the language of the MaxScript.
-Knowledge of the methods of three-dimensional
modeling of objects using basic and advanced
primitives, composite objects, modifiers and tools,
knowledge of the three-dimensional modeling of
objects using splines and shapes; knowledge of
polygon modeling, knowledge about the methods of
animation, lighting and rendering.
-The ability to simulate three-dimensional scenes, set
up the user environment, the ability to work with
standard materials, the ability to create new materials,
apply a texture to an object, the ability to adjust the
camera, the ability to set and adjust the lighting in the
scene, the ability to create animations, the ability to
perform visualization of the Stage.
PCG3302
Programming in computer graphics
2 credits/
Pre: Pro 1305
1+0+1
The purpose of discipline is to familiarize students with the
creation and visualization of images using the software and
hardware PC. Computer graphics - one of the most rapidly
developing branches of modern science. In the area of interest
includes all the computer graphics aspects of the formation and
image processing using hardware and software computer
systems. It covers all types and formats of images. The modern
world is built on total computerization and the widespread use
of information systems, it is difficult to imagine without the
computer graphics and its ability to create virtual reality and
visualization of scientific research.
-knowledge of software and hardware to create and
image processing on the PC, knowledge about
modern application programming interfaces (API)
-Ability to work with some of the application
programming interfaces (Open GL).
FRDBD3303
Fundamentals of relational database design
3 credits/
Pre: IT 1103, Pro 1305
Basic knowledge of the organization of relational databases
and tools for developing custom applications, you must for the
modern specialist, whose work is related to the processing of
large volumes of information, or to direct the design and
implementation of information systems in various institutions
or enterprises. The aim of the course is the development of
principles of relational databases and data capture techniques.
Since the the main tool to work with DDB is the language of
SQL, the task of discipline is the development of programming
skills in that language. In addition, the objectives of the course
also include getting the skills of designing relational databases.
As a theoretical basis for structuring the data in the RDB to the
task of the course also includes learning the basics of relational
algebra.
-Basic knowledge of the organization of relational
databases, and custom application development tools
necessary for a modern specialist, whose activities are
related to the processing of large volumes of
information or direct the design and implementation
of information systems in various institutions or
enterprises.
-The ability to build a relational database
Modules individual educational trajectories (IET)/ OC
IET 1. Mathematical Modeling
SW
Scientific writing (каз/рус/анг)
1 credits/
Pre:
1+0+0
SVA 2501
Spectral and wavelet analysis
2 credits/
Pre: MA 1301, MA 1303
1+1+0
The course is devoted to the latest trend in the theory and
practice of processing functions and signals - wavelet analysis.
The theory of wavelets appeared in the 90s of last century, and
rapidly developing countries, mainly in the Far Abroad. It
formed the basis for new methods and technologies of
compression and conversion of signals and images, has found
its application in medicine, geology, and telecommunications.
In its application the significance of the wavelet analysis is
comparable with the value of series and Fourier transforms,
while having a number of advantages. The course introduces
the basic concepts of wavelet - and the analysis of typical
examples show the characteristic features and applications of
wavelet analysis. Also in the course deals with methods of
spectral analysis of time series, the concept of filters, examples
of applications of spectral methods in the numerical solution of
multidimensional linear problems, examples of applications in
the theory of inverse problems.
-Knowledge of the function and wavelet analysis and
the ability to describe the transformation and
formation of signaling information, the principles of
decomposition signal convolution signal frequency
representation of signals;
-The ability to master the methods of sampling and
reconstruction of continuous signals, information data
interpolation
methods,
strengthening
and
development of the skills acquired through the study
of basic subjects areas such as mathematical analysis,
numerical methods, equations of mathematical
physics.
MMHPC 3502
Models and methods for highly productivetion
calculations
3 credits/
Pre:
2+0+1
The purpose of discipline - the study of mathematical models
and methods for solving problems in hydrodynamics for high-
performance systems. In the lecture materials include original
scientific publications domestic and foreign authors in peer-
reviewed journals. The course content is the author's
development based on existing literature on the subject and
experience of the development of parallel applications for
solving large computational problems.
to
gain
knowledge
about
the
methods
of
programming parallel virtual machines to master
some of parallel programming; know arhitekruru
cluster
systems,
be
able
to
make
parallel
programming code for any task, to acquire the skills
to construct an algorithm for solving the problem of
modeling a particular process with the use of high
performance computing.
MMGF2503
Mathematical modeling of geophysics
3 credits/
Pre: MA 1301, MA 1303, Pro 1305
2+0+1
The aim of the course to gain knowledge about universal
properties of Geophysics and how they are modeling,
mathematical models of Geophysics, used mathematical
methods. Geophysics in the broad sense is studying the physics
of solid Earth physics of the oceans.
Analyze mathematical models of Geophysics, using
mathematical methods and computers.
Strengthen and develop the skills learned in the study
of basic disciplines direction, such as the equations of
mathematical
physics,
numerical
methods,
programming languages
Have the skills, personality and problem-based
learning various topics of the course as part of
seasonal schools, special seminars, conferences and
student clubs.
SMTPh3504
Spectral Methods in Theoretical Physics
3 credits/
Pre: MA 1301, MA 1303
2+0+1
The aim of the course is the study of numerical algorithms and
spectral methods for solving problems in theoretical physics
and the ability of choice and application of spectral methods to
solve applied problems.
Spectral methods are often combined with other optical
methods for studying trends in theoretical physics. Spectral
methods, and sensitive method is used not only in theoretical
physics but also widely used in analytical chemistry,
astrophysics, metallurgy, mechanical engineering, geological
exploration, archeology and other fields of science.
Know the differential equations, the equations of
mathematical
physics,
numerical
methods,
programming languages C / C or Fortran, calculus,
based on mathematical modeling, spectral and
wavelet analysis
Be able to choose and use spectral methods for
applications, the ability to operate a computer and use
a programming language, the ability to restrain the
rational solution of the problem, the ability to use
scientific, reference, systematic literature on the
subject
Be skilled in the construction of mathematical models
of physical processes, sampling differential equations
of mathematical physics, to choose the correct
spectral numerical method to write the code for the
constructed mathematical models, graphs and
animations to the results, the development of the
personal qualities of self-training, to expand their
knowledge of mathematical and computer modeling
physical processes by means of spectral methods.
MMBPGE3505
Mathematical modeling biological processes and
Genetic Engineering
3 credits/
Pre: MA 1301, MA 1303, Pro 1305
1+2+0
This course is directed to studying mathematical models of
genetic engineering, training in formulating and solving of
mathematical problems, analyze the studying processes. In this
discipline is studied the mathematical models of processes of
selection of genes from an organism (cells), manipulation of
genes and introducing them to others. With respect to those
considered in the course objectives are described mathematical
approaches to the analysis of the behavior being studied
multivariable, nonlinear physical-chemical and biological
systems.
-Knowledge of the properties of molecular dynamics
and genetic engineering methods and their modeling;
-Ability to analyze mathematical models of
biomedical processes using mathematical methods
and computers;
strengthening and development of the skills acquired
through the study of basic subjects areas, such as the
equations of mathematical physics, numerical
methods, programming languages
Mathematical modeling of chemical processes
Problems which can be characterized as non-stationary tasks of
-Knowledge of modeling of chemical processes,
MMChP3506
3 credits/
Pre: MA 1301, MA 1303, Pro 1305, UMPh 2311
2+0+1
heat - and mass transfer at presence of dynamic sources of
substances and heat are examined in course. The concrete
solution of these problems is complicated owing to their
nonlinearity and parameters number large. However frequently
it is enough to investigate particular cases when in a complex
of the phenomena it is possible to leave out some of them and
to examine the simplified models. Conformity of the last to
real process is checked by the coordination of the received
solutions with the data of numerical and physical experiments.
At studying the simplified models it is possible to investigate
the basic features of process to define influence of parameters,
to study the critical phenomena, auto-oscillations, multiplicity
of processes regimes etc.
mathematical models of reactors, numerical models
of reactors features of writing the code for the task.
-The ability to make the code for modeling chemical
processes, to find a rational solution to the problem,
use scientific, background, methodological literature
on the subject, a mathematical model for the problem
of chemical-engineering process.
MMPhTP4507
Mathematical
modeling
of
physical
and
technological processes
3 credits/
Pre: MA 1301, MA 1303, Pro 1305, UMPh 2311
2+0+1
Considered in the course of the problem can be described as
time-dependent problems the heat - and mass transfer in the
presence of dynamic sources of substances and heat. The
specific solution of these problems is difficult because of their
non-linearity and mnogoparametrichnosti. Often, however, it
suffices to study the extreme cases when a complex set of
phenomena can abstract from some of them and consider the
simplified model. Compliance with the latest real process
checks the consistency of the solutions obtained with the data
of numerical and physical experiments. In the study of
simplified models can identify the main features of the process,
to determine the influence of parameters, to study critical
phenomena, self-oscillation, the multiplicity of modes of
processes, etc.
Course objectives: To study the characteristics and principles
of mathematical modeling of chemical processes, the
acquisition of knowledge and skills of students in the
development of mathematical models, the skills of their
simplicity and qualitative analysis of the dynamics of the
process and its use for the planning of field and numerical
experiments.
Knowledge of the principles and mathematical
modeling of chemical processes,
The ability to identify the main features of the
process, to determine the influence of parameters, to
study critical phenomena, self-oscillation, the
multiplicity of modes of processes
possess the skills of facilitation and qualitative
analysis of the dynamics of the process and its use for
the planning of field and numerical experiments.
CFD4508
Computational fluid dynamics
3 credits/
Pre: MA 1301, MA 1303, Pro 1305, UMPh 2311
2+0+1
Computational Fluid Dynamics - Subsection continuum
mechanics, which includes a combination of physical,
mathematical and numerical methods designed to calculate the
characteristics of flow processes. The basis of any research in
the field of computational fluid dynamics is the formulation of
the basic equations of hydro / gas dynamics of flow, namely,
the continuity equation, momentum equation, energy equation,
the equation of state (for gases)
will have knowledge about the methods of
formulation and numerical solution of problems
will have the skills to build the finite-difference
approximations of the computer computational
experiments;
will have in-depth knowledge of the fundamentals of
computational fluid dynamics;
will be able to apply this knowledge to solve and
The aim of the course study of the various methods and
processes of the above solutions of systems of equations.
analyze problems.
will have an understanding of modern application
programming interfaces (API) and be able to work
with some of them (Open GL, DirectX);
will have knowledge about the basic functions of the
API and be able to use them when writing the code
for creating and converting graphic images;
will be skilled in graphics programming and
visualization of realistic images.
MNDDM4509
Modeling the nonlinear dynamics of deformable
media
3 credits/
Pre: MA 1301, MA 1303, Pro 1305, UMPh 2311
1+2+0
The aim of the course to study the properties of non-linear
dynamical systems, besides the study of the general properties
and the laws of motion of deformable bodies, and force
interactions in these bodies.
Nonlinear dynamics is used to describe systems of non-linear
models, usually described by differential equations and
discrete maps. Nonlinear dynamics includes stability theory,
the theory of dynamical chaos, ergodic theory, the theory of
integrable systems.
Know the basic processes of the dynamics of
deformable media.
be able to: carry out a correct statement of the
problems of solid mechanics, be able to analyze the
efficiency of algorithms approximation of solutions
of nonlinear problems, select adequate scheme of
solving problems;
Possess the skills of systems of nonlinear models are
usually described by differential equations and
discrete maps
MMTPh4510
Mathematical models in theoretical physics
3 credits/
Pre: MA 1301, MA 1303, Pro 1305, UMPh 2311
2+0+1
In
recent
years, has
come understood
that a
lot
of
physical theories,
in
principle, the
subject
of geometry
in general. In physics operate with phase spaces of the state, in
geometry - the space of points. In geometry, a widely
used fiber bundles. It turned out that the theory of gauge fields
of Yang-Mills presents some fiber bundles. The aim of the
course is
to
familiarize students with
these,
as
well
as many other problems of theoretical physics.
Knowledge of the mathematical models used in
theoretical physics, knowledge of basic concepts,
theorems of theoretical physics knowledge of
methods for solving problems in theoretical physics
Ability to select appropriate mathematical model to
describe the mechanical processes, the ability to use
appropriate techniques to solve problems in
theoretical physics, the ability to analyze the results
from the point of view of physics . Possession of
skills in solving problems in theoretical physics
analysis of the results.
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