Bachelor’s programme

Bachelor's programme

01.03.01 Mechanics and mathematical modelling

  • The graduates obtain Bachelor degree
  • The bachelor’s degree program is 240 credits.
  • It takes four years to earn a bachelor’s degree.
Description of the program
Сurriculum

The field of professional activity of graduates

  • research activities in areas using mathematical methods and computer technology;
  • solving various problems using mathematical modeling of processes and objects and software;
  • development of effective methods for solving problems of natural science, engineering, economics and management;
  • IT support of scientific, research, design and operational management activities;
  • teaching mathematical disciplines (including computer science).

Disciplines

Math

Probability theory is the branch of mathematics that studies random events and quantities. Mathematical statistics is based on probability theory. It develops methods of registration, description and analysis of observations and experiments with the aim of building probabilistic models of mass random phenomena. The course covers the theoretical foundations, basic methods and approaches of probability theory and mathematical statistics.

 

Course: 4, terms: 4-8, hours: 180.

Mathematical analysis is the branch of mathematics dealing with analysis of infinitely small quantities, differential and integral calculus. The course introduces concepts and methods for such mathematical objects as derivatives, antiderivatives, integrals, limits, series. Mathematical analysis is the basis for the study of special courses.

 

Courses: 1-2, terms: 1-4, hours: 756.

Algebra is the branch of mathematics devoted to the study of operations on elements of sets of arbitrary nature, which generalizes the usual operations of addition and multiplication of numbers. The course focuses on linear algebra, which studies vector spaces, linear mappings, and systems of linear equations. The main mathematical tools of the course are determinants, matrices, conjugation.

 

Course: 1, terms: 1-2, hours: 288.

Analytic geometry is the branch of geometry, in which geometric shapes and their properties are investigated by means of algebra tools.

 

Course: 1, term: 1, hours: 144.

The course is devoted to the study of methods of differential equations investigation. These equations include the derivatives of the function, can include the function itself, the independent variable and parameters. The course focuses on ordinary differential equations. Differential equations are widely used in mechanics and physics.
 
Course: 2, terms: 3-4, hours: 252.
 
Functional analysis is a branch of mathematics in which the spaces of functions and their mappings are studied. The axioms of linear normed space, metric and Hilbert spaces, the notions of a mapping and a functional, an operator, a spectrum and a resolvent of an operator, differentiation in Banach spaces are studied.
 
Course: 3, terms: 5, hours: 108.
 
The theory of functions of a complex variable is the branch of mathematical analysis that investigates functions of complex numbers. Analytic functions, conformal mappings, complex integrals, Riemann surfaces, series of analytic functions are studied in this course.

Course: 3, terms: 5-6, hours: 216.

 
The course is devoted to the study of differential geometry and topology objects: smooth manifolds, flat lines and curves, spatial curves and lines, the theory of surfaces, affine properties of lines and surfaces, elements of field theory.

Course: 2, term: 3, hours: 144.

 
Calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals. Various methods and algorithms for finding the minimum of the cost function in a certain region of a finite-dimensional bounded vector space are considered in the course.

Course: 4, term: 7, hours: 216.

 
Mathematical physics – the theory of mathematical models of physical phenomena. Partial differential equations, their classification and solution methods are studied in this course.

Course: 3, terms: 5-6, hours: 216.

 
The basics of set theory, binary relations, mathematical logic, combinatorics and combinatorial schemes, graph theory, theory of algorithms are studied. The course introduces students to discrete mathematics applications related to information technology and computers.

Course: 1, term: 1, hours: 144.

Tensor analysis is a section of tensor calculus that studies differential operators acting on the algebra of tensor fields of a differentiable variety. In the course, the basic concepts of vector and tensor analysis, the mathematical apparatus of tensor algebra, necessary for solving theoretical and practical problems are studied

Course: 2, term: 3, hours: 108.

The basic concepts, models and methods of computational mathematics, the numerical methods of their applied aspects arising in the computational problems of mathematics and mechanics are studied. 

Elective course: Numerical methods / The finite element method in problems of mechanics

Course: 3, term: 6, hours: 144.

Mechanics and Physics

The theoretical foundations of classical physics, methods for solving practical problems, the methodology for conducting research in the field of physics are studied here. The course forms students’ skills in the practical application of a physical and mathematical apparatus in various fields of physics and technology.
 
Courses: 2-3, terms: 2-3, hours: 288.
Theoretical mechanics is the science of the simplest forms of movement and interaction of material bodies. The course includes sections of kinematics, statics, dynamics, and the theory of impact.
 
Course: 2, terms: 3-4, hours: 504.
 
Analytical mechanics is a section of theoretical mechanics in which the general principles of mechanics are formulated, equations of motion and methods for their integration are derived and investigated on their basis. The Lagrange, Hamilton, Raus, Appell, Whittaker, Jacobi equations are studied.
 
Course: 3, term: 5, hours: 252.
Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of gaseous, liquid and deformable solids, as well as force interactions in such bodies. The course studies the basic laws of the kinematics of continuous deformable environment, the laws of motion of continuous deformable environment, a linear elastic body, and a linear viscous fluid; basic concepts and equations of thermodynamics of continuous environment.

Course: 3, term: 6, hours: 108.

The theory of similarity and the method of dimensions, the basic mathematical models in fluid and gas mechanics, incompressible potential flows, methods for calculating supersonic flows with compression shocks and Prandtl-Meier flow characteristics, wing profile characteristics, methods for finding potential flow lines are studied.

Course: 4, term: 7, hours: 180.

The course introduces students to the program of bachelor “Mechanics and Mathematical Modeling”, with the history of development and modern areas of research in the field of mathematics and mechanics, the structure of the Samara University, the organization of the educational process at the university and the University’s research in the field of mathematics and mechanics.

Course: 1, term: 2, hours: 144.

The course introduces students to the modern state of mechanics as a science. It forms the skills of using modern methods of theoretical mechanics in the framework of fundamental and applied problems, as well as the skills of independent scientific research in the field of mechanics and the interpretation of the results.

Course: 4, terms: 7-8, hours: 216.

The theory of sustainability, studies the behavior of systems under the influence of external influences. The course studies the basic methods of the theory of stability and theorems on stability and instability of motion.

Course: 3, terms: 5-6, hours: 261.

Mechanics of deformable solid body is a part of continuum mechanics that studies the change in the shape of solids during external and internal influences and motion. The course introduces students to mathematical models, the modern mathematical apparatus of the mechanics of a deformable solid, and various models of the mechanical behavior of environments.

Course: 3, terms: 5-6, hours: 216.

 
The course forms students’ skills in applying modern mathematical packages for solving problems of mathematics and mechanics. The workshop aims to consolidate the theoretical knowledge gained in professional disciplines with practical examples.
 
Course: 2, term: 3, hours: 72.
 
The course forms the skills of applying the methods of numerical simulation and modern computing software for solving problems of mechanics. The workshop is aimed at consolidating the skills of developing and writing mathematical models using modern computing software.
 
Course: 3, term: 6, hours: 72.
 
The basics and methods of celestial mechanics, the laws of the motion of celestial bodies, the elements of the orbit, the methods of determining orbits from observations, the types of motion of planets, satellites, asteroids, comets, the basics of the theory of motion of artificial satellites of the Earth are studied in this course.
 
Elective course: Elements of celestial mechanics / Theory of elasticity
 
Course: 3, term: 6, hours: 108.
 
The basic concepts of the theory of elasticity as an integral part of the mechanics of a deformable solid, the results and methods for solving the problems of the theory of elasticity as a fundamental science that underlies many modern technologies are studied in this course.

Elective course: Elements of celestial mechanics / Theory of elasticity

Course: 3, term: 6, hours: 108.

Fluid properties, flow models, Navier-Stokes equations and numerical methods for solving problems of fluid and gas mechanics in the Mathcad application software package are studied. 

Elective course: Databases / Numerical solution of problems in fluid and gas mechanics in an application package Mathcad

Course: 3, term: 6, hours: 108.

 
The course introduces students to the basics of the finite element method, finite-element solutions to problems of continuum mechanics, and the SIMULIA Abaqus software package, which allows to obtain accurate and reliable solutions to the most complex problems of deformable solid mechanics.

Elective course: Numerical methods / The finite element method in problems of mechanics

Course: 3, term: 6, hours: 144.

Autonomous control systems and their characteristics, typical dynamic links, methods for studying the stability of linear automatic control systems, the quality analysis of linear control systems and their synthesis are studied in this course. 

Elective course: Automatic control theory / Mathematical models in the mechanics of a deformable solid

Course: 4, term: 7, hours: 180.

Mathematical models in the mechanics of a deformable solid, methods for calculating the stress-strain state of bodies and structures beyond the elastic limits, methods for analytic and numerical solving problems of the theory of creep, elastic-plastic, visco-elastic problems are studied in this course. 

Elective course: Automatic control theory / Mathematical models in the mechanics of a deformable solid

Course: 4, term: 7, hours: 180.

 
Analytical methods are studied for the approximate solution of problems of nonlinear mechanics, in particular the methods of Poincaré, van der Pol, averaging, the method of large parameter.

Elective course: Asymptotic methods in nonlinear mechanics / Numerical methods in fluid and gas mechanics

Course: 4, term: 8, hours: 144.

The Navier-Stokes equations, numerical methods for solving problems in fluid and gas mechanics, in particular, the finite difference method, the sweep method, and numerical methods for solving problems in the Mathcad application package are studied in this course. 

Elective course: Asymptotic methods in nonlinear mechanics / Numerical methods in fluid and gas mechanics

Course: 4, term: 8, hours: 144.

 
Oscillation theory considers oscillations of mechanical systems using the apparatus of differential calculus. The course studies the theoretical foundations and methods of the theory of oscillations for practical application in solving scientific, research and practical problems.

Elective course: Oscillation theory / Solving problems of continuum mechanics using modern software packages

Course: 4, term: 7, hours: 144.

 
The course examines the use of algorithms and methods for solving practical problems of continuum mechanics.

Elective course: Oscillation theory / Solving problems of continuum mechanics using modern software packages

Course: 4, term: 7, hours: 144.

Methods for solving typical problems of mechanics of a deformable solid are studied using engineering analysis programs. 

Elective course: Engineering methods in deformable solid mechanics / Information technology in the problems of mechanics

Course: 4, term: 8, hours: 108.

The course introduces students to methods for solving nonlinear equations of mathematical physics and mechanics, with the analysis of dimensions and the physical similarity of the phenomena of the surrounding world; with scaling laws and auto-similar solutions of the first and second kind. 

Elective course: Applied problems of rigid body dynamics / Automodel solutions of equations of mathematical physics

Course: 4, term: 8, hours: 144.

Computer science

The course introduces students to the principles of working with a personal computer, office suites and TeX system. The course forms the computer skills necessary for further study and research, the ability to publicly present our own and well-known scientific results.

Course: 1, term: 1, hours: 108.

The course provides students with ideas about the graphic capabilities of modern computers, vector and raster images, programs for graphical representation of graphs and diagrams, packages for working with 3D graphics. Course: 2, term: 4, hours: 144.
The course aims to form an understanding of modern integrated mathematical packages (Maple, Wolfram Mathemtica, Matlab) and methods of using them to solve problems of science and technology. Courses: 2-3, terms: 4-5, hours: 216.
The basic principles of programming, techniques and skills for solving problems, modern programming technologies are being studied. The course is aimed at developing students’ skills in solving problems of a wide domain with the help of programming tools. Elective course: Technology and programming languages / Multiprocessor computing Course: 1, terms: 1-2, hours: 252.
Methods for creating parallel programs for multiprocessor computing systems, architectural principles for implementing parallel processing in computing machines, language mechanisms for designing parallel programs, systems for developing parallel programs are being studied in the course. Elective course: Technology and programming languages / Multiprocessor computing Course: 1, terms: 1-2, hours: 252.
The main technologies of database development, modern instrumental and methodological development tools, structured query language SQL are studied in the course. Elective course: Databases / Numerical solution of problems in fluid and gas mechanics in an application package Mathcad Course: 3, term: 6, hours: 108.
The course is aimed at developing knowledge of the skills and abilities to use information technologies for solving mechanical problems. Elective course: Engineering methods in deformable solid mechanics / Information technology in the problems of mechanics Course: 4, term: 8, hours: 108.

General courses

The history of Russia, the laws of historical development, historical facts and events, outstanding historical figures are studied in the course. The aim of the course is the formation of historical consciousness and civic consciousness, the ability to use the knowledge and skills gained in solving social and professional tasks. Course: 1, term: 2, hours: 108.
The history of philosophy, the nature and role of philosophical knowledge in the development of modern civilization, the subject and specificity of philosophical thinking, the basic categories of philosophy, methods of posing theoretical questions, their analysis and solution are studied. Course: 2, terms: 3-4, hours: 144.
The basic concepts, laws and methods of economic theory, algorithms, techniques and tools for solving economic problems and tasks are studied. The course lays the foundation for mastering the disciplines of socio-economic direction. Course: 3, term: 6, hours: 108.
The grammatical basis of a foreign language is studied. Abilities and readiness for intercultural communication, speaking and writing skills, skills of conducting business and personal correspondence in a foreign language are formed. Courses: 1-2, terms: 1-4, hours: 288.
The basic concepts of political science, types of political culture, the nature and significance of civic culture for a democratic society, the content and stages of political socialization of the individual, the role and importance of politics in the life of society are studied. Course: 4, term: 7, hours: 72.
The structure of Russian law, the fundamentals of the state’s activities and the realization of citizens’ rights, the specifics of regulation of legal relations, the legal framework for professional activities are studied in the course Course: 4, term: 8, hours: 72.

The theoretical and methodical and practical bases of physical culture and a healthy lifestyle are studied.

Courses: 1-3, terms: 1-6, hours: 400.

The main medical and hygienic aspects of human life, the reserves and capabilities of the body, methods for identifying hazardous and harmful factors that are consequences of accidents, catastrophes, natural disasters and means of protection against them are studied in the course. Course: 4, term: 7, hours: 108.