Course: Complex Analysis - Exercises

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Course title Complex Analysis - Exercises
Course code MU/01921
Organizational form of instruction Lesson
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 2
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • ENGLIŠ Miroslav, prof. RNDr. DrSc.
  • MLÍCHOVÁ Michaela, RNDr. Ph.D.
Course content
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.

Learning activities and teaching methods
unspecified
Recommended literature
  • E. Kreyszig. Advanced Engineering Mathematics. Wiley, New York, 1983.
  • P. V. O'Neil. Advanced Engineering Mathematics. Wadsworth Publishing Company, Belmont, 1983.
  • R. V. Churchill, J. W. Brown, R. F. Verhey. Complex Variables and Applications. Mc Graw-Hill, New York, 1976.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Mathematics (2014-IVT) Mathematics courses 2 Summer
Mathematical Institute in Opava Mathematics (1-IVT) Mathematics courses 2 Summer
Mathematical Institute in Opava Mathematics (2014-F) Mathematics courses 2 Summer
Mathematical Institute in Opava Mathematics (2-F) Mathematics courses 2 Summer