MU03027 Complex Analysis

Mathematical Institute in Opava
Winter 2020
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Miroslav Engliš, DrSc. (lecturer)
RNDr. Lenka Rucká, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Miroslav Engliš, DrSc.
Mathematical Institute in Opava
Prerequisites (in Czech)
TYP_STUDIA(BN)
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Students will acquire basic knowledge of complex analysis needed for further study of mathematics, as well as for completing the course of Complex Analysis. Contents of the course cover part of the requirements specified for the Final State Examination.
Syllabus
  • Prerequisites: holomorphic functions, Cauchy formula, power series. Infinite products.
    Extended complex plane. Meromorphic functions.
    Homology forms of Cauchy theorems, simple connectedness. Argument principle.
    Conformal mapping, linear fractional maps, Riemannn mapping theorem.
    Analytic continuation, Riemann surfaces - basic theory.
    Harmonic functions, Poisson integral. Laplace transform and its applications.
Literature
    recommended literature
  • J. Smítal. Komplexní analýza. MÚ SU, Opava, 2008. info
  • W. Rudin. Analýza v reálném a komplexním oboru. Academia, Praha, 1987. info
  • E. Kreyszig. Advanced Engineering Mathematics. Wiley, New York, 1983. info
  • R. V. Churchill, J. W. Brown, R. F. Verhey. Complex Variables and Applications. Mc Graw-Hill, New York, 1976. info
  • I. Kluvánek, L. Mišík, M. Švec. Matematika II. SNTL, 1961. info
  • I. I. Privalov. Úvod do teorie funkcí komplexní proměnné. Fizmatgiz, 1960. info
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
Teacher's information
Requirements for pre-exam credits are set out by the tutorial lecturer. In principle, they should warrant sufficient mastery of the course content.
The same applies to the written part of the exam. The oral part of the exam verifies cognisance of basic concepts of the theory.
The course is also listed under the following terms Winter 1997, Winter 1998, Summer 1999, Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2021, Winter 2022, Winter 2023, Winter 2024.
  • Enrolment Statistics (Winter 2020, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2020/MU03027