Master 2020/2021

Mathematics of Science

Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'

Type: Compulsory course (Mathematics)

Area of studies: Mathematics

Delivered by: Department of Fundamental Mathematics

Where: Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod)

When: 1 year, 1-4 module

Mode of studies: offline

Instructors: Efim Pelinovsky

Master’s programme: Mathematics

Language: English

ECTS credits: 6

Contact hours: 72

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

• 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

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

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

• Control work
• Exam
• Control work
• Exam

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

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