2020/2021
Research Seminar "Complex Analysis"
Category 'Best Course for Career Development'
Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
3, 4 module
Instructors:
Vladimir Andreevich Poberezhny
Language:
English
ECTS credits:
6
Contact hours:
72
Course Syllabus
Abstract
The course is aimed to formation of structured analytical thinking of students and their acquaintance with the basic concepts and methods of complex analysis. The course is based on introductory courses of real analysis, geometry, differential equations and smooth manifolds. The knowledge and skills gained in mastering the discipline can be usefull for studying such courses as Hamiltonian mechanics, Field theory, Complex geometry, Riemann surfaces, PDE analysys and many others
Learning Objectives
- The course is aimed to formation of structured analytical thinking of students and their acquaintance with the basic concepts and methods of complex analysis. The course is based on introductory courses of real analysis, geometry, differential equations and smooth manifolds.
Expected Learning Outcomes
- Formation of structured analytical thinking. Acquaintance with the basic concepts and methods of complex analysis.
Course Contents
- Complex differentiability
- Linear fractional transformations
- Analytical functions
- Laurent series
- Isolated singular points
- Residues
- Complex integrability
Bibliography
Recommended Core Bibliography
- Basic complex analysis, Marsden, J. E., 1999
- Complex analysis : an introduction to the theory of analytic functions of one complex variable, Ahlfors, L. V., 1979
- Narasimhan, R. (1985). Analysis on Real and Complex Manifolds. Amsterdam: North Holland. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=342519
- Real and complex analysis, Rudin, W., 1987
Recommended Additional Bibliography
- Complex analysis, Lang, S., 2003