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"Mechanics and Mathematical Modeling" (bachelor's degree). Basic physical models and concepts of mechanics Organizations in which graduates work

Basic questions of mechanics

Kinematics

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

Under the mechanical movement we will understand the 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 movement of a given material object are as follows:

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 otherwise ?, that is, what are the reasons that cause exactly this species and the nature of the movement of the object in question?

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

Conclusions: mechanical movement relatively and is the simplest form the 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 this particular situation can be neglected or not.

For example, considering the motion of the Earth around the Sun, it can be considered a material point, since the radius of the Earth R z = 6400 km is much 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 own axis it is impossible to apply the “material point” model for the Earth.

When studying the motion of a body or a 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, the movement of which needs to be studied, is mentally divided into small sections (material points), the dimensions of which are much smaller than the dimensions of the body or system of bodies. In this case, the study of the motion of a body or a system of bodies is reduced to the study of the motion of individual sections of the system, that is, the material points that make up this system. In this case, one should, of course, take into account whether the material points interact with each other or not.



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

Solid - is a system of material points, mutual arrangement which does not change during this movement.

Pay attention to 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 conditions. A perfectly 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 An imaginary line along which a given material point moves is called.

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

Translational called such a motion of a rigid body, in which any straight line, fastened to this body, during its movement remains parallel to itself.

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

rotational called such a motion 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 movement”. Trajectories are either straight or curved. The motion of a rigid body can be reduced to two forms: translational and rotational.

During the training, students acquire scientific knowledge on computer modeling of various mechanical processes, develop the ability to think analytically, learn to put into practice the basics of fundamental mathematics, mechanics, physics and other natural sciences.

Graduates find application for 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" - a direction that allows in the future to make a choice from quite a large number interesting professions:

    Researcher,

  • mathematician,

    analyst,

    supervisor,

    researcher,

    teacher of physical and mathematical disciplines,

    specialist in mathematical modeling.

Direction characteristics

Characteristic Index
Training leads
Level of training Undergraduate
Direction code 01.03.03
Total number of budget places 25
of which places for persons with special right 3
Number of paid places 25
Entrance tests Informatics and ICT — 42
Russian language - 40
Mathematics - 39
Priority entrance examinations Mathematics; Informatics and information and communication technologies (ICT); Russian language.
Competition for budget places in 2019 8,50
The minimum total score when crediting to the budget in this area in 2019 216
Graduation qualification Bachelor
Form of study full-time
Term of full-time study 4 years
Cost of full-time education RUB 139,707 (in 2019)

Syllabus

Basic specialized disciplines:

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

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

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 named after. Christianovich, VTB-24 bank, Sibnats OJSC, UNI-KONKord LLC, Cryosphere Institute of the Earth SB RAS, Rusgazproekt OJSC, Nizhneobsky NIPI OJSC, Giprotumenneftegaz OJSC, Infa CJSC, Surgutnipineft, NPO fundamental GAZPROMPRECTING ", LLC" IngeoService, LLC Kogalymnipineft.

Achievements

  • The TSU SPE Student Chapter team (as part of D.V. Balin) reached the finals of the student intellectual game PetroBowl in London.
  • Victory in the contest of the best student works Danil Balin - "The impact of the auto-fracturing process on the development of the field", scientific. head M.Yu. Danko, Head of Hydrodynamic Modeling Department, CJSC Tyumen Institute of Oil and Gas

Learning Outcomes

    Ability to decide challenging tasks method of 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 problems of mechanical modeling without the participation of a PC (if the situation requires it).

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

    Organization of pedagogical, scientific, managerial and production-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 of bachelors:

Siberian and Ural Branch of the Russian Academy of Sciences, Central Bank, Sberbank of Russia OJSC, Zapsibkombank OJSC, Surgutneftegazbank OJSC, SibNIINP OJSC, Schlumberger, Tyumen Institute of Oil and Gas LLC, TyumenNIPIGIPROGAZ LLC, Gazprom Neft OJSC, VostokNefteGazProekt CJSC, ITAM SB RAS named after I.I. Christianovich, VTB-24 bank, Sibnats OJSC, UNI-KONKord LLC, Cryosphere Institute of the Earth SB RAS, Rusgazproekt OJSC, Nizhneobsky NIPI OJSC, Giprotumenneftegaz OJSC, Infa CJSC, Surgutnipineft, NPO fundamental GAZPROMPRECTING ", LLC" IngeoService, LLC Kogalymnipineft.

Internships for students, undergraduates and graduate students:

  • Evgeny Popov – Scholarship of the President of the Russian Federation for studying abroad, Center for Cloud Computing, University of Birmingham (Great Britain);
  • Artem Vorobyov - Scholarship of the President of the Russian Federation for studying abroad, Nanyang Technological University (Singapore);
  • Alexander Kropotin - Scholarship of the President of the Russian Federation for studying abroad, Ulm University (Germany);
  • Alexander Stupnikov - Scholarship of the President of the Russian Federation for studying abroad, Ulm University (Germany);
  • Natalia Derevyasnikova - program "Semester Abroad", University of Passau (Germany);
  • Artur Romazanov, Evgenia Egorova - program "Semester Abroad", University of Passau (Germany);
  • Andrey Rybkin - program "Semester Abroad", Kindai University (Gosaka, Japan);
  • Anna Zhikhareva - Global UGRAD student exchange program, University of Idaho at Boise (USA);
  • Ekaterina Lobanova – Fulbright FLTA Program, Wheaton College (Norton, USA)
  • Alexander Gorbachev - Fulbright Program, State Research University (New York State, USA);
  • Natalia Derevyasnikova, Anton Lyachek – internship, Huawei (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, Research Fellow at the Cloud Computing Center at the University of Birmingham (Great Britain), holder of grants from the President of the Russian Federation, the Potanin Foundation, Governor's Scholarships, Winner of IT-Planet and WorldSkills Russia competencies "Network and system administration"
  • Mikhail Fuchko, WorldSkills Russia National Expert in Network and System Administration, coach of the WorldSkills Russia National Team, Head. laboratory of network and system administration of Tyumen State University.
  • Elena Tolubaeva, head of department information technologies Federal Tax Service of Russia for the Kurgan Region
  • Ivan Karyakin, director of IT company Mintrocket
  • Pavel Mostovoy, Leading Specialist of the Large Exploration Projects Support Department, Gazprom Neft Science and Technology Center
  • Anna Semenova, specialist of the information and analytical department of the MAOU "Information and Methodological Center"
  • Olga Chuenko, Deputy Director of the GKU TO "Center for Information Technologies of the Tyumen Region"
  • Maria Krovatkina, network engineer, Schlumberger Logelco inc (Europe and Africa)
  • Inna Grigorieva, head of Department of Business Process Automation (based 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 Program and systems engineering, Ph.D.
  • Yulia Boganyuk, head. computer laboratories IMiKN, winner of the regional competition scientific works, winner of the contest "Miss IT of the Tyumen Region", WorldSkills Russia expert in the "Machine Learning and BigData" competency
  • Igor Mashchitsky, Data Processing Specialist at SAP IT-SERVICE LLC (SIBUR)
  • Andrey Sorokin, Head of the Processing Group, Operational Support for Seismic Surveys, Gazpromneft NTC LLC
  • Sergey Glazunov, one of the most famous white hat hackers in Russia. For his work on finding Chrome vulnerabilities, Google paid him more than $80,000,
  • Andrey Labunets, specialist of the information security department of Facebook
  • Alexander Gorbachev, winner and prize-winner of national championships, WorldSkills World Championship, European Championship in the nomination of system administration, grant holder for master's studies in the USA.
  • Irina Prudaeva, Deputy Director of the Department for the 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 Business Software Solutions competency
  • Andrey Evdokimov, Technical Specialist, 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, IMS Service under the Administration of Gazprom Dobycha Urengoy
  • Evgeny Kabardinsky, Software Engineer at Leadex Systems
  • Konstantin Borisov, Chief Specialist of the Department of Master Planning and Production Calculation, Gazpromneft-Yamal LLC
  • Nikita Pogodin, Java developer at Luxoft
  • Abdullah Bashiru, Project Manager software Alsart (Lagos/Nigeria)
  • N.S. Bakhtiy, Head of the Department of Mathematical Modeling of Oil and Gas Fields, SurgutNIPIneft, Ph.D.
  • A.A. Zolotov, Development Director of the Club of IT Directors of the Tyumen Region, Head of the Information Systems Development Department of Concord Soft LLC
  • I.N. Polishchuk, director of the Tyumen branch of JSC "GIS-ASUproject", Ph.D.
  • V.V. Trofimov, Development Director, PJSC Rostelecom branch in the Tyumen and Kurgan regions
  • A. Parkhomtsev, Director of LLC "Louis + Western Siberia"
  • A.P. Devyatkov, Associate Professor, Department of Fundamental Mathematics and Mechanics, IMiKN, Ph.D.
Foreign partner universities
  • Northeast Pedagogical University (China).
  • Qufu State Pedagogical University (China).
  • University of Passau (Germany).
  • University of Münster (Germany).
  • graduate School administrative sciences, Speyer (Germany).
  • Tallinn University (Estonia).
  • Daugavpils University (Latvia).
  • Novobolgarsky University of Sofia (Bulgaria).
  • University. Humboldt in Berlin.
  • University of Navarra (Spain).
  • University of Strasbourg (France).
  • University of Lorraine, Metz (France).
  • University of Toulouse 2 - Le Miray (France).
  • Bodo University College (Norway).
  • University of Oslo (Norway).
  • University of Wolverhampton (UK).
  • University of California, Los Angeles (USA).
  • Federal University of Fluminense (Brazil).
  • Cooperation agreement between federal agency for the Commonwealth of Independent States, compatriots living abroad, and for international humanitarian cooperation (Rossotrudnichestvo).
  • Eurasian humanitarian Institute(The Republic of Kazakhstan).
  • Yerevan public university(Republic of Armenia).
  • Tashkent University of Information Technologies.
  • University of Informatics and Information Technologies. Apostle Paul, Ohrid.
  • University of Lüneburg.

Partner companies
  • Microsoft, Samsung
  • Zapsibkombank
  • SKB Kontur
  • OOO "Tyumen Institute of Oil and Gas"
  • Base Group Labs

Institute of Mathematics and Computer Science

Description

Students studying 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 continuous media, mechanics of a deformable solid body, robotics, hydroaeromechanics). In the learning process Special attention is given to workshops, including computer ones, where computational and experimental methods for studying the state and motion of material bodies are mastered. Depending on the chosen specialization, students may be interested in such disciplines as physical and chemical gas dynamics, biomechanics, the fundamentals of the nonlinear theory of thin-walled structures, problems of dynamic fracture, the theory of stability of plates and shells, methods for creating functional and nanostructured materials, etc.

Whom to work

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

Main results, results of work and plans for the future

Undergraduate

In 2015, the first graduation of bachelors took place in the direction with a profile "Experimental mechanics and computer simulation in mechanics". Eight people out of ten who entered the Department of TiPM in 2011 successfully defended their graduation theses and received bachelor's degrees in engineering.

The developed curriculum for the preparation of a bachelor in the direction "Mechanics and Mathematical Modeling" proved its high quality. In comparison with the previous program of the specialist in "Mechanics", non-core subjects were removed, the ratio between the physical and mathematical cycle of disciplines and special courses, the physical and mechanical workshop and the computational experiment was balanced. At the official level, training has been introduced to work with the universal "heavy" calculation complex ANSYS (ANSYSInc., USA), which is one of the three main finite element complexes used in industry to develop new technology. Based on the experience gained and in connection with the further development of the federal state educational standard the undergraduate curriculum will continue to improve and optimize for the needs of high-tech production.

As a result, the achieved level of mastering the basic educational program of the bachelor's graduate turned out to be higher than the specialist's graduate (4.1 vs. 3.8), and the presented bachelor's theses, despite the shorter preparation time, "beat" the diplomas of specialists (4.6 vs. 4.2). At the same time, the solved scientific and practical problems themselves aroused keen interest among the members of the state commission and lengthy discussions.

Master's degree

This year the first enrollment for the new master's program was carried out "Dynamics and strength of complex mechanical systems" directions "Mechanics and Mathematical Modeling". Nine people came to us, including graduates of the bachelor's degree program "Experimental Mechanics and Computer Simulation in Mechanics".

The bachelor's degree level is only the first level in the system of Russian and world education. It provides basic theoretical level and gives some practical experience. However, in order to solve the main task of the Russian industry today - the creation in the shortest possible time of globally competitive and demanded products of a new generation - specialists of a new formation are needed - "engineering and technological special forces", whose training can only be carried out on master's programs focused on the high-tech sector of the economy. This is the program we offer to our undergraduate students.

Engineers of the 21st century are research and development engineers who own all the world-class advanced technologies, are able to “break through walls”, “solve unsolvable problems”, make innovative breakthroughs, and ultimately ensure the creation of a new generation of industrial products.

Distribution, practice

The distribution this year has been more active than ever, which is associated with the end of the specialist's programs and the double graduation. However, there was no particular interest in specialist graduates compared to bachelor graduates. The "hunger" for the development engineers of new technology is only increasing. Mechanical engineers are in demand in all branches of mechanical engineering: heavy, energy, auto, ship, aircraft and rocket manufacturing. We were visited by both old partners (Galich Truck Crane Plant, Federal Nuclear Center - Scientific Research Institute of Technical Physics, Progresstekh-Dubna LLC, Gazpromtrubinvest OJSC), as well as new ones, among which the Experimental Machine-Building Plant named after A.I. Myasishchev, engaged in the creation of aviation, aerospace, aerostatic and landing equipment. It was there that most of the mechanical graduates of this year went to the design department for a very decent salary.

Industrial practice 3rd year bachelor's degree "Mechanics and Mathematical Modeling" went very well. After a long break, the students worked in the super-equipped materials testing laboratory of the Dipos Group of Companies (Ivanovo), in the Proton Innovation Center (Vladimir). I would especially like to note the practice at the enterprise "GosMKB" Raduga "named after. A.Ya. Bereznyak (Dubna), which produces high-speed aircraft, and in the Moscow engineering center of a large international company FESTO, Germany.

The profession lies at the intersection of mathematics, physics and computer science. Students learn to predict the physical processes occurring in solids, liquids, gases and plasmas using mathematical modeling methods. To do this, you have to use complex computer programs, and sometimes you have to create them yourself. Moreover, if it is impossible to use a computer, graduates should be able to solve the problem in other ways. IN curriculum Much attention is paid to physical disciplines, especially mechanics. Also, students get acquainted with computer science, programming and robotics. Specialization depends on what kind of objects the graduate decides to model: solids, liquids or gases. Such a branch of science as engineering biomechanics is becoming popular - the study of the properties of living tissues and design artificial parts body. *

* Kit academic disciplines and learning bias