Basic physical models and concepts of mechanics. “mechanics and mathematical modeling Mechanics and mathematical modeling work prospects

During their studies, students acquire scientific knowledge on computer modeling of various mechanical processes, develop analytical thinking abilities, and learn to apply in practice the fundamentals of fundamental mathematics, mechanics, physics and other natural sciences.

Graduates find application of their knowledge in engineering centers of industrial companies, gas and oil industries, transnational corporations, research and design bureaus involved in the development of new engineering technologies.

“Mechanics and mathematical modeling” is a direction that will allow you to choose from a fairly large number of interesting professions in the future:

    Researcher,

  • mathematician,

    analyst,

    supervisor,

    researcher,

    teacher of physical and mathematical disciplines,

    mathematical modeling specialist.

Direction characteristics

Characteristic Index
Training is conducted by
Level of training Bachelor's degree
Direction code 01.03.03
Total number of budget places 25
of which places are for persons with special rights 3
Number of paid places 25
Entrance tests Computer Science and ICT - 42
Russian language - 40
Mathematics - 39
Priority of entrance tests Mathematics; Computer Science and Information and Communication Technologies (ICT); Russian language.
Competition for budget places in 2019 8,50
Minimum total score for admission to the budget in this area in 2019 216
Graduate qualification Bachelor
Form of study Full-time
Duration of full-time study 4 years
Cost of full-time training RUB 139,707 (in 2019)

Syllabus

Basic profile disciplines:

  • mathematical analysis;
  • differential equations;
  • theoretical mechanics;
  • partial differential equations;
  • fluid dynamics;
  • numerical methods in continuum mechanics;
  • physics of oil and gas reservoir;
  • dynamic systems;
  • application packages;
  • dynamics of compressible media;
  • computer mathematics systems.

Classes are taught by full-time teachers: doctors and candidates of science:

Tatosov A.V. , professor, doctor of sciences;

Shalaginov S.D. , associate professor, candidate of sciences;

Machulis V.V. ,Associate Professor, Candidate of Sciences;

Mosyagin V.E. , associate professor, candidate of sciences;

Devyatkov A.P. , associate professor, candidate of sciences;

Butakova N.N. , associate professor, candidate of sciences;

Basinsky K.Yu. , associate professor, candidate of sciences.

Practices

Siberian and Ural Branch of the Academy of Sciences of the Russian Federation, OJSC Sberbank of Russia, OJSC Zapsibkombank, Schlumberger, LLC Tyumen Institute of Oil and Gas, LLC TyumenNIPIGIPROGAZ, ITAM SB RAS. Khristianovich, Bank VTB-24, JSC SibNATs, LLC UNI-CONCORD, Institute of the Earth's Cryosphere SB RAS, JSC Rusgazproekt, JSC Nizhneobsky NIPI, NPO Sibtekhneft, JSC Giprotyumenneftegaz, JSC INFA , SurgutNIPINeft, NPO Fundamentstroyarkos, Gazpromproektirovanie LLC, Ingeoservice LLC, KogalymNIPINeft LLC.

Achievements

  • The TSU SPE Student Chapter team (consisting of D.V. Balin) reached the finals of the student intellectual game PetroBowl in London.
  • Victory in the competition for the best student works Danil Balin - “The influence of the auto-fracturing process on field development”, scientific. head M.Yu. Danko, head of the hydrodynamic modeling department of JSC Tyumen Institute of Oil and Gas

Learning outcomes

    Ability to solve complex problems using information and communication technologies.

    Use of mathematical analysis in the field of theoretical and applied mechanics, geometry, differential equations and probability theory.

    Work with specialized programs for modeling and optimization of technological processes.

    Doing research work independently or in a group.

    Solving mechanical modeling problems without the participation of a PC (if the situation requires it).

    Adapting your knowledge to the organization of the educational process in your field of competence (physics, mechanics, mathematics, computer science).

    Organization of pedagogical, scientific, managerial, production and technological activities.

Employment and career

Areas of activity:

Bachelors have the opportunity to work in any field of science, industry, production, management related to mathematics, engineering, physics, mechanics and programming.

Places of employment for bachelors:

Siberian and Ural Branch of the Academy of Sciences of the Russian Federation, Central Bank, Sberbank of Russia OJSC, Zapsibkombank OJSC, Surgutneftegazbank OJSC, SibNIINP OJSC, Schlumberger, Tyumen Institute of Oil and Gas LLC, TyumenNIPIGIPROGAZ LLC, OJSC Gazpromneft", CJSC "VostokNefteGazProekt", ITAM SB RAS named after. Khristianovich, Bank VTB-24, JSC SibNATs, LLC UNI-CONCORD, Institute of the Earth's Cryosphere SB RAS, JSC Rusgazproekt, JSC Nizhneobsky NIPI, NPO Sibtekhneft, JSC Giprotyumenneftegaz, JSC INFA , SurgutNIPINeft, NPO Fundamentstroyarkos, Gazpromproektirovanie LLC, Ingeoservice LLC, KogalymNIPINeft LLC.

Internships for students, undergraduates and graduate students:

  • Evgeny Popov – RF Presidential Scholarship recipient for studying abroad, Cloud Computing Center University of Birmingham (UK);
  • Artem Vorobyov – RF Presidential Scholarship recipient for studying abroad, Nanyang Technological University (Singapore);
  • Alexander Kropotin – scholarship holder of the President of the Russian Federation for studying abroad, Ulm University (Germany);
  • Alexander Stupnikov – scholarship holder of the President of the Russian Federation for studying abroad, Ulm University (Germany);
  • Natalya Derevyasnikova – “Semester Abroad” program, University of Passau (Germany);
  • Arthur Romazanov, Evgenia Egorova – “Semester Abroad” program, University of Passau (Germany);
  • Andrey Rybkin – “Semester Abroad” program, Kindai University (Osaka, Japan);
  • Anna Zhikhareva – Global UGRAD student exchange program, Idaho State University at Boise (USA);
  • Ekaterina Lobanova – Fulbright FLTA program, Wheaton College (Norton, USA)
  • Alexander Gorbachev – Fulbright program, State Research University (New York State, USA);
  • Natalya Derevyasnikova, Anton Lyachek – internship, Huawei company (Shenzhen and Beijing, China);
  • Polina Gultyaeva, Vladislav Fishman – “Semester Abroad” program, University of Koblenz-Landau (Germany)
  • Lusine Harutyunyan, Mikhail Lyapunov – “Semester Abroad” program, University of Guadalajara (Mexico)
  • Maria Rudzevich, Director of the Department of Informatization of the Tyumen Region
  • Garif Romashkin, manager of the regional bank VTB24
  • Evgeny Popov, researcher at the Cloud Computing Center at the University of Birmingham (UK), winner of grants from the President of the Russian Federation, Potanin Foundation, Governor's Scholarship, winner of IT Planet and WorldSkills Russia in the “Network and System Administration” competency
  • Mikhail Fuchko, national expert at WorldSkills Russia in the “Network and System Administration” competency, coach of the WorldSkills Russia national team, head. Laboratory of Network and System Administration of Tyumen State University.
  • Elena Tolubaeva, head of the information technology department of the Federal Tax Service of Russia for the Kurgan region
  • Ivan Karyakin, director of the IT company Mintrocket
  • Pavel Mostovoy, leading specialist of the department for support of large geological exploration projects, Gazprom Neft Scientific and Technical Center
  • Anna Semenova, specialist of the information and analytical department of the MAOU "Information and Methodological Center"
  • Olga Chuenko, Deputy Director of the State Public Institution TO "Information Technology Center of the Tyumen Region"
  • Maria Krovatkina, network engineer at Schlumberger Logelco inc (Europe and Africa)
  • Inna Grigorieva, head. Basic Department of Business Process Automation (on the 1C:Enterprise platform), Ph.D.
  • Vladislav Shkabura, developer, Schlumberger
  • Alexander Blazhenskikh, developer at Yandex.Cloud
  • Mikhail Grigoriev, national expert of WorldSkills Russia, associate professor of the department of software and systems engineering, Ph.D.
  • Yulia Boganyuk, head. computer laboratories of IMiKN, winner of the regional competition of scientific works, winner of the Miss IT Tyumen Region competition, WorldSkills Russia expert in the “Machine Learning and Big Data” competency
  • Igor Maschitsky, data processing specialist at SAP IT-SERVICE LLC (SIBUR)
  • Andrey Sorokin, head of the processing group, department of operational support of seismic exploration works of Gazpromneft Scientific and Technical Center LLC
  • Sergei Glazunov, one of the most famous white hat hackers in Russia. Google paid him more than $80,000 for his work searching for Chrome vulnerabilities.
  • Andrey Labunets, information security department specialist at Facebook
  • Alexander Gorbachev, winner and prize-winner of national championships, World Skills World Championships, European Championships in the system administration category, grant holder for master's studies in the USA.
  • Irina Prudaeva, Deputy Director of the Office for Implementation of Programs and Projects Information and Methodological Center
  • Elena Sycheva, development engineer, Tyumen Institute of Oil and Gas
  • Tatyana Yuferova, winner of the WorldSkills Russia Tyumen, WorldSkills Russia Ural, WorldSkills Russia National Championships in the “Software Solutions for Business” category
  • Andrey Evdokimov, technical specialist of the Department of technological support for standardized procedures for assessing student achievements, TOGIRRO
  • Yuri Egorov, leading development engineer at Baspro Group of Companies
  • Anna Kozhevnikova, software engineer of the I&C Service under the Gazprom Dobycha Urengoy Administration
  • Evgeny Kabardinsky, Software Engineer at Leadex Systems
  • Konstantin Borisov, Chief Specialist of the Department of Consolidated Planning and Production Calculation, Gazpromneft-Yamal LLC
  • Nikita Pogodin, Java developer at Luxoft
  • Abdullah Bashiru, Alsart Software Manager (Lagos/Nigeria)
  • N.S. Bakhtiy, Head of the Department of Mathematical Modeling of Oil and Gas Fields at SurgutNIPIneft, Ph.D.
  • A.A. Zolotov, development director of the Tyumen region CIO Club, head of the information systems development department of Concord Soft LLC
  • I.N. Polishchuk, Director of the Tyumen branch of JSC GIS-ASUproekt, Ph.D.
  • V.V. Trofimov, Development Director, Rostelecom PJSC branch in the Tyumen and Kurgan regions
  • A. Parkhomtsev, director of Louis+ Western Siberia LLC
  • A.P. Devyatkov, Associate Professor of the Department of Fundamental Mathematics and Mechanics of the Institute of Computer Science and Technology, Ph.D.
Foreign partner universities
  • Northeast Normal University (China).
  • Qufu State Normal University (China).
  • University of Passau (Germany).
  • University of Münster (Germany).
  • Graduate School of Administrative Sciences Speyer (Germany).
  • Tallinn University (Estonia).
  • Daugavpils University (Latvia).
  • New Bulgarian University of Sofia (Bulgaria).
  • University named after Humboldt in Berlin.
  • University of Navarra (Spain).
  • University of Strasbourg (France).
  • University of Lorraine Metz (France).
  • University of Toulouse 2 – Le Mirail (France).
  • Bodo University College (Norway).
  • University of Oslo (Norway).
  • University of Wolverhampton (UK).
  • University of California, Los Angeles (USA).
  • Federal University of Fluminense (Brazil).
  • Agreement on cooperation between the Federal Agency for the Commonwealth of Independent States, compatriots living abroad, and international humanitarian cooperation (Rossotrudnichestvo).
  • Eurasian Humanitarian Institute (Republic of Kazakhstan).
  • Yerevan State University (Republic of Armenia).
  • Tashkent University of Information Technologies.
  • University of Informatics and Information Technologies named after. Apostle Paul, Ohrid.
  • University of Lüneburg.

Partner companies
  • Microsoft, Samsung
  • Zapsibcombank
  • SKB Kontur
  • LLC "Tyumen Institute of Oil and Gas"
  • BaseGroup Labs

Institute of Mathematics and Computer Science

The most common entrance exams:

  • Russian language
  • Mathematics (basic level)
  • Physics is a specialized subject, at the choice of the university
  • Computer science and information and communication technologies (ICT) - at the university's choice

Professions

“Mechanics and mathematical modeling” is a specialty that allows you to choose from a fairly large number of interesting professions in the future:

  • Researcher,
  • engineer,
  • mathematician,
  • analyst,
  • supervisor,
  • researcher,
  • teacher of physical and mathematical disciplines,
  • mathematical modeling specialist.

Academic bachelors have the opportunity to work in any field of science, industry, production, management related to mathematics, engineering, physics, mechanics and programming.

Description of specialty

During their studies, students acquire scientific knowledge on computer modeling of various mechanical processes. Students study computational mathematics, mechanics and biomechanics, the theory of stability of electromechanical devices, the degree of elasticity, density and plasticity of materials. They also master the static and dynamic strength of various objects and other sciences, one way or another related to theoretical mechanics, mathematics, engineering, and strength materials.

During the learning process, students develop analytical thinking abilities, study the fundamentals of economics and production management, and learn to apply in practice the fundamentals of fundamental mathematics, mechanics, physics and other natural sciences.

A special feature of training in the specialty “Mechanics and Mathematical Modeling” is a large number of standard hours devoted to workshops. Where students have a unique opportunity to apply their theoretical knowledge in practice, analyze and synthesize specific information. Some of the workshops are devoted to working with computer-mathematical modeling programs designed to simulate technological processes on a monitor screen.

Graduates find application of their knowledge in engineering centers of industrial companies, gas and oil industries, transnational corporations, research and design bureaus, including foreign ones, involved in the development of new engineering technologies.

Basic subjects when studying for a specialty

  • Mechanics of deformable bodies and media.
  • Mathematical modeling and computer engineering.

In addition, students study philosophy, history, a foreign language and life safety (basics of life safety). Compulsory disciplines: physical education and applied physical education.

Duration of training

Duration of full-time education in the specialty"Mechanics and mathematical modeling" is 4 years (including holidays). Full-time and distance learning, by decision of the administration, can be extended for a period of six months to a year.

Skills and abilities acquired during training

  • Ability to solve complex problems using information and communication technologies.
  • Use of mathematical analysis in the field of theoretical and applied mechanics, strength of metals, geometry, differential equations and probability theory.
  • Work with specialized programs for modeling and optimization of technological processes.
  • Doing research work independently or in a group.
  • Solving mechanical modeling problems without the participation of a PC (if the situation requires it).
  • Adapting your knowledge to the organization of the educational process in your field of competence (physics, mechanics, mathematics, computer science).
  • Organization of pedagogical, scientific, managerial, production and technological activities.

During the course of training, the bachelor acquires the professional skills necessary for competent engineering and analysis of complex mechanical objects using computer and/or physical analysis.

Basic questions of mechanics

Kinematics

Mechanics studies the simplest forms of motion found in the material world, which are united under the general name, mechanical motion.

By mechanical movement we will understand a change in the relative position of one material object in relation to another material object. This is one of the most important properties of mechanical motion: its relativity.

The main questions that arise when trying to characterize the mechanical motion of a given material object are the following:

1. How does this object move?, that is, what is the type and nature of its relative motion?

2. Why does this object move this way and not another?, that is, what are the reasons that cause this particular type and nature of the movement of the object in question?

The search for an answer to the first of these questions is carried out by the section of mechanics - kinematics, and the second - dynamics.

Conclusions: Mechanical motion is relative and is the simplest form of motion of matter. Basic questions of mechanics: How and why does a material object move?

Depending on the properties of a material object, the nature and type of its movement, the simplest physical models are used in mechanics:

material point (particle) - an object (body), the dimensions of which can be neglected in comparison with the characteristic size of the movement in which this object participates.

Here we should pay attention to the relative nature of the concept and its abstractness. Any real object has finite dimensions, which in a given specific situation can or cannot be neglected.

For example, considering the movement of the Earth around the Sun, it can be considered a material point, since the radius of the Earth R s = 6400 km is significantly less than the radius of its orbit around the Sun R s = 1.5 × 10 8 km. On the other side,

When considering the daily rotation of the Earth around its own axis, it is impossible to apply the “material point” model to the Earth.

When studying the motion of a body or system of bodies, when the concept of a material point cannot be used, it is often useful to apply another physical model, which is called system of material points.

The essence of this model is that any body or system of bodies whose movement needs to be studied is mentally divided into small areas (material points), the dimensions of which are significantly smaller than the size of the body or system of bodies. In this case, the study of the movement of a body or system of bodies comes down to the study of the movement of individual sections of the system, that is, the material points of which this system consists. In this case, one should, of course, take into account whether the material points interact with each other or not.



A special case of the “system of material points” model in mechanics is the model called solid:

Solid - This is a system of material points, the relative position of which does not change during a given movement.

Note the relativity of this model.

The limiting case of a rigid body model is an absolutely rigid body. In an absolutely solid body, the distance between any arbitrary particles does not change under any circumstances. An absolutely rigid body is an abstract model, since no real body has this property.

To describe the movement of a material point, a model is used - trajectory .

Trajectory of movement is called an imaginary line along which the movement of a given material point occurs.

If this line is a straight line or its segment, then they say that the movement of the material point is rectilinear, otherwise the movement is curvilinear. To describe the types of motion of a rigid body, models of translational and rotational motion are used.

Progressive This is the movement of a rigid body in which any straight line attached to this body remains parallel to itself during its movement.

A characteristic feature of such movement is that the trajectories of all material points that make up a solid body have the same shape and size and, with parallel displacement, can be combined with each other.

Rotational is the movement of a rigid body in which all its material points move in circles. In this case, the centers of these circles are located on one straight line, called the axis of rotation.

Arbitrary motion of a rigid body can always be represented as a set of simultaneous translational and rotational motions.

Conclusions: The main physical models of mechanics are a material point, a system of material points and a rigid body. The movement of a material point is determined by the concept of “trajectory of motion”. Trajectories can be rectilinear or curvilinear. The motion of a rigid body can be reduced to two forms: translational and rotational.

Description

Students studying in this profile study the disciplines of the mathematical cycle (algebra, geometry, mathematical analysis), computer (databases, computer graphics, operating systems, programming languages, 3D graphics, parallel programming), as well as applied and theoretical sections of mechanics ( theoretical mechanics, mechanics of fluid, gas and continuum, mechanics of deformable solids, robotics, hydroaeromechanics). In the learning process, special attention is paid to workshops, including computer ones, in which computational and experimental methods for studying the state and movement of material bodies are mastered. Depending on the chosen specialization, students’ areas of interest may include such disciplines as physicochemical gas dynamics, biomechanics, fundamentals of the nonlinear theory of thin-walled structures, problems of dynamic destruction, theory of stability of plates and shells, methods for creating functional and nanostructured materials, etc.

Who to work with

Due to the fact that graduates of the profile receive fundamental training in mathematics and computer science, they can get a job both in the field of mechanics and in the field of computer technology. The first place of employment may be computer centers of large enterprises, educational institutions, for example, research institutes, computer firms, design bureaus of industrial organizations, universities and business and economic structures. In addition, during their studies, young people can engage in research work, take part in scientific conferences, competitions, seminars and olympiads, and subsequently continue their studies in a master’s program.

Speciality "Mechanics and mathematical modeling" is a branch of applied mathematics that deals with the mathematical modeling of complex physical processes in solids, liquids, gases and plasmas.

During their studies, students receive deep fundamental knowledge in the field of mathematics and programming, classical mechanics. In addition, students are taught a wide range of special disciplines in various areas of modern mechanics. The amount of training in the field of computer science, programming, and IT technologies is significant.

During their studies, students will learn:

  • Apply mathematical methods and algorithms of computational mathematics in solving mechanics problems and analyzing applied problems
  • Participate in research seminars, conferences, symposia, as well as organize them
  • Prepare scientific articles and scientific and technical reports
  • Process general scientific and scientific-technical information
  • Apply fundamental knowledge in the field of mechanics when preparing and conducting experimental studies
  • Conduct research work in the field of mechanics and mathematical modeling
  • Conduct experimental research in mechanics
  • Use specialized software systems to solve mechanical problems
  • Analyze the results of research, production and technological activities
  • Teach physical and mathematical disciplines and computer science in general education and secondary vocational educational institutions with specialized retraining

A significant proportion of graduates devote themselves to research careers. But the direction also has practical applications. In production, specialists can be involved in calculating power and thermal loads on the surface of aircraft, creating new materials and alloys with shape memory effect, designing installations for the production and transportation of oil and gas, etc. Specialists in mechanics and mathematical modeling are required in research institutes and centers, mining enterprises, and aircraft design bureaus.

Assigned qualification

Mechanic. Applied mathematician - professional qualification of a specialist

Positions held

  • Programmer
  • Mechanical Engineer
  • Mathematician
  • Mathematics teacher
  • Mathematical Modeling Specialist

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