MU20021 Analysis in the Complex Domain

Mathematical Institute in Opava
Summer 2021
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michaela Mlíchová, Ph.D. (lecturer)
Mgr. Jakub Šotola (seminar tutor)
Guaranteed by
prof. RNDr. Miroslav Engliš, DrSc.
Mathematical Institute in Opava
Timetable
Wed 13:05–14:40 118
  • Timetable of Seminar Groups:
MU20021/01: Wed 17:15–18:50 RZ, J. Šotola
Prerequisites (in Czech)
MU20003 Mathematical Analysis III && TYP_STUDIA ( B )
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 Analysis in the Complex Domain.
Syllabus
  • 1. Complex numbers, analytic functions - algebraic and goniometric form of a complex number; curves and domains in the complex plane; derivatives of functions of complex variable; analytic functions; Cauchy-Riemann equations; exponential and trigonometric functions; logarithm.
    2. Conformal mapping - linear transformations, Moebius transformations, exponential function, logarithm.
    3. Integration in the complex domain - integrals over curves, Cauchy theorem, Cauchy formula.
    4. Power series in the complex domain - Taylor series, Laurent series, singularities and roots.
    5. Integration using residue theorem - residues, residue theorem, evaluation of integrals.
Literature
    required literature
  • W. Rudin. Real and complex analysis. New York, 1987. ISBN 0-07-100276-6. info
    recommended literature
  • Smítal. Komplexní analýza. MÚ SU, Opava, 1999. info
  • R. V. Churchill, J. W. Brown, R. F. Verhey. Complex Variables and Applications. Mc Graw-Hill, New York, 1976. 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.

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