M7270 Complex analysis II

Faculty of Science
autumn 2021
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. Ilja Kossovskij, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 14:00–15:50 M3,01023
  • Timetable of Seminar Groups:
M7270/01: Fri 12:00–13:50 M6,01011, I. Kossovskij
Prerequisites
Calculus of one and several variables, basic complex analysis
Course Enrolment Limitations
The course is offered to students of any study field.
Abstract
This is an advanced course in complex analysis of one and several variables.
Learning outcomes
At the end of the course students should be able to:
understand basic differences between complex analysis in one and several variables
use integral representations of holomorphic functions for deriving their properties and boundary behaviour
understand properties and use of Bergman kernel and Bergman projection
master techniques for solving nonhomogeneous Cauchy-Riemann equations
Key topics
  • The argument principle
  • the Rouché theorem
  • Hartogs phenomenon
  • Integral reprezentation of holomorphic functions,
  • Bergman kernel and projection
  • Solutions of inhomogeneous Cauchy-Riemann equations
  • Foundations of CR geometry
Study resources and literature
  • RANGE, Michael R. Holomorphic functions and integral representations in several complex variables. 2nd corr. print. New York: Springer-Verlag, 1998, xv, 388 s. ISBN 0-387-96259-X. info
Approaches, practices, and methods used in teaching
Lectures, exercises, homeworks
Method of verifying learning outcomes and course completion requirements
oral exam
Language of instruction
Czech
Further Comments
Study Materials
The course is taught once in two years.
The course is also listed under the following terms Autumn 2019, Autumn 2023, Autumn 2025.
  • Enrolment Statistics (autumn 2021, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2021/M7270