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Магистратура 2020/2021

Математические методы естествознания

Лучший по критерию «Полезность курса для расширения кругозора и разностороннего развития»
Статус: Курс обязательный (Математика)
Направление: 01.04.01. Математика
Когда читается: 1-й курс, 1-4 модуль
Формат изучения: без онлайн-курса
Прогр. обучения: Математика
Язык: английский
Кредиты: 6

Course Syllabus

Abstract

The course is dedicated to mathematical methods of Theory of Dynamical Systems and their applications to some problems of Natural Science. The main attention concerns with physical and biological problems. The course aims to prepare students to work with applications of mathematical methods to some areas of natural science.
Learning Objectives

Learning Objectives

  • The course aims to prepare students to work with applications of mathematical methods to some areas of natural science, and familiarization with actual scientific problems related to physics and biology.
Expected Learning Outcomes

Expected Learning Outcomes

  • Invesigation of 2-body problem.
  • Deduction of Euler hydrodynamic equation.
  • Investigation of Andronov oscillator.
  • Investigations of two-dimensional Lottka-Voltera system.
Course Contents

Course Contents

  • Applications of dynamical systems in Celestial Mechanics
    Copernicus heliocentric system. Kepler's laws. The problem of two body solved vy Isaak Newton.
  • Application of dynamical systems in Hydrodynamics
    Euler and Bernulli equations in hydrodynamics
  • Mathematical models of oscillators.
    Linear oscillators. Nonlinear oscillators by Van der Pole and Andronov.
  • Applications of dynamical systems in Biology
    The model predator-prey. Lotka-Volterra equations.
Assessment Elements

Assessment Elements

  • non-blocking Control work
  • non-blocking Exam
  • non-blocking Control work
  • non-blocking Exam
Interim Assessment

Interim Assessment

  • Interim assessment (2 module)
    0.3 * Control work + 0.7 * Exam
  • Interim assessment (4 module)
    0.3 * Control work + 0.7 * Exam
Bibliography

Bibliography

Recommended Core Bibliography

  • - A Few Lessons from American History: Reader for Students of English - Общество с ограниченной ответственностью «Издательство «СТАТУТ» - 2014 - 80с. - ISBN: 978-5-8354-1011-8 - Текст электронный // ЭБС ЛАНЬ - URL: https://e.lanbook.com/book/61518
  • - AutoCAD 2010. Официальный учебный курс - Издательство "ДМК Пресс" - 2010 - 694с. - ISBN: 978-5-94074-613-3 - Текст электронный // ЭБС ЛАНЬ - URL: https://e.lanbook.com/book/1322

Recommended Additional Bibliography

  • Conee, E. B., & Sider, T. (2014). Riddles of Existence : A Guided Tour of Metaphysics: New Edition (Vol. New edition). Oxford: OUP Oxford. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=864690