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Regular version of the site
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
When: 1 year, 1-4 module
Mode of studies: offline
Instructors: Efim Pelinovsky
Master’s programme: Mathematics
Language: English
ECTS credits: 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

• 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.

• 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

#### 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