Course: Analysis in the Complex Domain

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Course title Analysis in the Complex Domain
Course code MU/01022
Organizational form of instruction Lecture
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 4
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
  • ENGLIŠ Miroslav, prof. RNDr. DrSc.
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
Recommended literature
  • E. Kreyszig. Advanced Engineering Mathematics. Wiley, New York, 1983.
  • J. Smítal, P. Šindelářová. Komplexní analýza. MÚ SU, Opava, 2002.
  • 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.
  • W. Rudin. Analýza v reálném a komplexním oboru. Academia, Praha, 1987.

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 (2014-F) Mathematics courses 2 Summer