M7270 Complex analysis II

Faculty of Science
Autumn 2023
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. Ilja Kossovskij, 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 MS1,01016
  • Timetable of Seminar Groups:
M7270/01: Thu 12:00–13:50 MS1,01016, 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.
Course objectives
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
Syllabus
  • 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
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
Teaching methods
Lectures, exercises, homeworks
Assessment methods
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 2021.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2023/M7270