Mathematics of Science

2023/2024

Academic Year

ENG

Instruction in English

6

ECTS credits

Delivered at:

Department of Fundamental Mathematics (Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod))

Course type:

Compulsory course

When:

1 year, 3, 4 module

Instructor

Pelinovsky, Efim

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

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

Course Contents

• Applications of dynamical systems in Celestial Mechanics
• Application of dynamical systems in Hydrodynamics
• Mathematical models of oscillators.
• Applications of dynamical systems in Biology

Assessment Elements

• kontrol work
• exam

Interim Assessment

• 2023/2024 4th module
  0.7 * exam + 0.15 * kontrol work + 0.15 * kontrol work

Bibliography

Recommended Core Bibliography

• Cortés, V., & Haupt, A. S. (2016). Lecture Notes on Mathematical Methods of Classical Physics. https://doi.org/10.1007/978-3-319-56463-0
• Fuente, A. de la. (2000). Mathematical Methods and Models for Economists. Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.b.cup.cbooks.9780521585293
• Strogatz, S. H. (2000). Nonlinear Dynamics and Chaos : With Applications to Physics, Biology, Chemistry, and Engineering (Vol. 1st pbk. print). Cambridge, MA: Westview Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=421098

Recommended Additional Bibliography

• Farach-Colton, M. (1999). Mathematical Support for Molecular Biology : Papers Related to the Special Year in Mathematical Support for Molecular Biology, 1994-1998. AMS.
• Gusfield, D. (1997). Algorithms on Strings, Trees, and Sequences : Computer Science and Computational Biology. Cambridge University Press.

Authors

• Pelinovskii Efim Naumovich