ANNOTATION OF DISCIPLINE
010400.68 "Applied Mathematics and Informatics"
M2.Б.2 Discrete and Mathematical Models
Umber of ECTS credits allocated: 3cr.
classroom load:
0,94 cr.
independent load: 1,06 cr.
Semester: 10th
The department of Applied Mathematics
The Institute of Mathematics, Information and Space Technologies
Type of course unit: Compulsory
Level of course unit: First cycle
Mode of delivery: Distance learning
Module «Discrete and mathematical models» is aimed at developing students' skills in research and
modeling of complex dynamic systems and processes in nature, technology and society, with the help of
equations (differential, difference, etc.). The importance of these skills is very high because the modeling
makes it possible to investigate the system, analyze the various options for its behavior, make long-term
forecasts without interfering with the system itself, and to experiment without material cost. At the stage
of building a model is analyzed accuracy of the model, adequacy and sustainability for its further use. But
people have always sought to find the best solution to the problem (maximum of profit, minimum of time,
minimum of material costs), they want to control a process. Therefore it is important to teach students to
build a driven model and look for the most optimal control of the system or process to achieve their aims.
This course covers a very interesting and important for our region matter: the modeling of Arctic
ice, the modeling of growth of the forest, the dynamics of the epidemic, the modeling of fishing , the
modeling of biological processes, etc.
The tasks typically are global and require not only powerful mathematical tools, but also
programming skills and use of various mathematical packages for computer modeling. In module
«Discrete and mathematical models» are proposed methods for the numerical approximation and
algorithmic task, solution methods and interpretation of the results.
Place of module in the curriculum:
Discipline M2.Б.2 "Discrete and mathematical models" refers to the base part of the professional
cycle. Discipline is taught in the fifth year (in the tenth semester). Module "Discrete and Mathematical
Models" is one of the components of the theoretical and practice-oriented training of students in direction
"Applied mathematics and informatics." For the successful study of the course "Discrete and
mathematical models" the student should know the basic concepts and positions of disciplines:
mathematical analysis, mathematical logic and discrete mathematics, numerical analysis, optimization
methods, basics of functional analysis and to know how to use the software packages Maple-16,
MatCAD-13 , Visual Studio-2010. The study of this training course is the basis for the further successful
study of disciplines: organization of information services, operations research, optimal control of complex
dynamic systems.
The aim of the study of course " Discrete and mathematical models": the formation of
student's ideas about the methods of construction, research and use of mathematical models in areas such
as medicine, social and economic life, physics, engineering, ecology.
Tasks of the discipline:
- to consider the classical models used in medical, social and economic life, physics, engineering,
ecology;
- learn the techniques for design and analysis of simulation models in these spheres;
- learn how to build logically reconciled reasoning;
- learn how to use the methods of mathematical modeling for the formalization and application solutions;
- get the ability to work independently and be able to find and process additional information in a given
subject area.
The results of the mastering the discipline:
Mastering the discipline provides the formation of students of general cultural (ОК-1, ОК-2, ОК-3, ОК-4,
ОК-6, ОК-7) and professional (ПК-1-13, ПК-15, ПК-17, ПК-18, ПК-24, ПК-26) competencies provided
by the federal state educational standard of higher education in the field of study "Applied mathematics
and information."
As a result of the mastering the discipline the student must
know:
- the basic models of physics, socio-economic and biomedical processes,
- the basic principles of modeling systems and processes;
- statistical methods of data processing to find the system parameters;
- the methods of research of the stability of systems;
-methods of numerical approximation;
be able to:
- construct a continuous and discrete, deterministic and stochastic, one-dimensional or multi-dimensional
model of a system or process to be studied;
- investigate the stability of the model;
- explore a model for the adequacy and accuracy;
- find the model parameters using empirical data;
have:
- skills to build models of systems and processes;
- skills to research models of systems and processes;
- skills of programming in C, C + +, C #;
- skills to work with packages Maple, MathCad, MathLab.
Summary of the module:
Concept and types of mathematical modeling, examples. Working out of mathematical models based on
the conservation laws, variational principles and analogies. Construction of mathematical models
(deterministic and stochastic, continuous and discrete, one-and n-dimensional, uncontrollable and
controled) of medicine, social and economic life, physics, engineering, ecology.
Forms of control: the laboratory work, tests.
The list of literature:
1.
Dvoretsky S.I., Muromtsev J.L., Pogonin V.A., Skhirtladze A.G. Modeling of systems. Moscow:
Academy / Series: Higher education. 2009. - 242 p.
2.
Ablanskaya L.V., Babeshko L.O., Bausov L.I. and other. Economic-mathematical modeling.
Moscow: Exam / Series: Textbook for high schools. 2011.-254 p.
3.
Zarubin V.S. Mathematical modeling in techniques. MSTU named after N. Bauman / Series:
Mathematics at the Technical University. 2010. – 206 p.
4.
Kermack W., Mc. Kendrick A. The contribution to the mathematical theory of epidemics, Proc.
Roy. Soc. London, 1927,115,1932,138,1933,141; J. Hyg., Cambridge, 1937,37,1939.
5.
Kloeden P.E, Platen E. Kloeden solution of stochastic differencial equation. Berlin: SpringerVarlag, 1992, 632p.
6.
Kloeden P.E, Platen E., Schurz H. Numerical solution of SDE through computer experiments.
Berlin: Springer-Varlag, 1994, 292p.
7.
Anderson R.M., May R.M. Infectious diseases of People: Dynamics and the Control. Oxford
University Press: Oxford, 1991.
8.
Wall N. A.: the Mathematical Theory of Epidemics: London, 1957.
9.
Behncke H.: the Optimum Control of determined Epidemics. Applied and Methods 2000; 21269285.
10. Cesari L.: the Theory of optimization and Application. Springer: New York, 1983.
11. Heesterbeck J.A., Metz J.A.J. A saturation contacts to norm in Marchriage and epidemic models, J.
Mathematics. Biol. 1993, 31529-539.
12. Hethcote H.W.: One thousand and one epidemic models. Mathematics. Biology, S.A. Levin
(editor)., Notes of Lecture in Miomathematics, the edition 100. Springer: Berlin, Heidelberg, 1994.