Předmět Complex analysis 1 (KMA / WKOA1)
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Další informace
Obsah
Programme of the Course1.Complex numbers, algebraic and geometric properties. Algebraic and exponential form of a complex number. Moivre Theorem.2.Metric in complex plane. Neighborhood, interior points, boundary points. Accumulation points, isolated points. Open and closed sets. Connected sets, regions. Plane curve and its parametrization. Closed curve. Jordan Theorem.3.Limit of a sequence of complex numbers. Complex functions, continuity.4.Differentiability, basic properties. Holomorphic functions. The Cauchy-Riemann equations.5.Möbius transformation and its properties. Infinity and the cross ratio. Stereographic projection.6.Exponential function and its properties.7.Trigonometric functions, properties.8.Logarithmic functions, properties.9.Inverse trigonometric functions. General power functions, exponential functions and logarithmic functions.10.Definition of integral along a plane curve and basic properties. Length of a smooth curve.11.Cauchy Theorem. Cauchy?s Integral Formula and its applications.
Literatura
Beck, M. A first course in Complex Analysis.
Požadavky
Examination: 100 points are available for the final examination, which has a written part with a possible oral explanation of particular questions that may arise based on the written exam. The evaluation of the course including the classification is carried out in accordance with the Study and Examination Regulations OU.
Garant
doc. RNDr. Ladislav Mišík, CSc.
Vyučující
doc. RNDr. Ladislav Mišík, CSc.doc. RNDr. Ladislav Mišík, CSc.