2020/2021
Научно-исследовательский семинар "Комплексный анализ"
Лучший по критерию «Полезность курса для Вашей будущей карьеры»
Лучший по критерию «Полезность курса для расширения кругозора и разностороннего развития»
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
3, 4 модуль
Преподаватели:
Побережный Владимир Андреевич
Язык:
английский
Кредиты:
6
Контактные часы:
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