Master
2023/2024
Mathematics of Science
Category 'Best Course for Career Development'
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
When:
1 year, 3, 4 module
Mode of studies:
distance learning
Online hours:
42
Open to:
students of one campus
Instructors:
Efim Pelinovsky
Master’s programme:
Mathematics
Language:
English
ECTS credits:
6
Contact hours:
84
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
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.