## MATHEMATICAL MODELS AND THEIR APPLICATIONS

 Course unit code В.2.2 Course unit title Options Name(s), surname(s) and title of lecturer(s) Olga P. Fedorova, Candidate of Physico-Mathematical Sciences, Associate Professor Andrey A. Bart, Candidate of Physico-Mathematical Sciences, Associate Professor Term 2 ECTS credits 5 Working hours Contact hours lectures 64 Self-study 116 Total 180 Work placement Laboratory works in Computer class Prerequisites It is assumed that the students have mastered the following disciplines «Mathematical Analysis», «Linear Algebra», «Differential Equations», », «Probability Theory and Mathematical Statistics», «Numerical Methods»? «Differential geometry», «Computer sciences and programming languages» and «Continuum mechanics». Language of instruction English (Russian) Objectives of the course Learning outcomes A student’s assessments methods 1. Preparation of undergraduate of mathematics to applying mathematical methods, model approach, and numerical experiment for solving applied problems in the professional work. 2. To give an experience in applying the knowledge’s acquired in courses of mathematical analysis, differential geometry, differential equations, partial differential equations, probability theory, numerical methods, and computer sciences in: - Formulation of problems, - Analytical study of these problem using mathematical models, - Formulation of differential models, - Choosing a numerical method, - Creation of algorithms and programs in a high-level language, - Carrying out a numerical experiment, - Representation of results of simulations. After drawing on the course «Mathematical models and their applications», the student must: Know main differential models and ways of their construction; Be able to understand the posed problem, intelligently use the language of the subject domain, form a mathematical model, adequately choose the method for resolving the model, and formulate the result; Have skills in analytical study of models, applying MATLAB for a software implementation of an algorithm, carrying out a numerical experiment, and visual representation of investigation results. The current control of mastering the discipline includes three written tests and five reports on the labs, three individual tasks and the final control – exam. Teaching methods Lectures, Labs List of Topics Topic title Contact hours Assignments and independent study hours Introduction 4 Written test № 1 Mathematical models 4 Written test № 1 Elements of the embedded language of the MATLAB environment 0 Written test № 2 Examples of forming simplest mathematical models 6 Individual task №1, Lab 1 Basic concepts of mathematical modeling 4 Written test № 3, Individual task №1 Model of the equivalent electric circuit 6 Lab 2, Individual task №2 Lotka--Volterra mathematical model 6 Lab 3 Basic differential equations of heat exchange in a real medium 6 Individual task №3 Boundary layer approximation 12 Lab 4 Boundary problem resolution algorithm at the stagnation point 10 Lab 5 Assessment requirements In during the semester 40 points Assessment criteria Each lab 4 points, each individual task 5 points and each test 3 points The composition of final accumulative mark Exam 56 points. Examination ticket consists of two theoretical questions (10x2=20) and two exercises (18x2=36). Author of the course Olga P. Fedorova