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Lecturer(s)
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Course content
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1. Foundations of the complex analysis revised 2. Index of a point with respect to a curve 3. Cauchy theorem 4. Cauchy formula 5. Qualitative properties of holomorphic functions 6. Fundamental theorem of algebra 7. Power series expansion 8. Laurent series 9. Calculus of residues 10. Conformal mappings 11. Computation of conformal mapping 12. Laplace transform 13. Laplace transform solution methods in the theory of differential equations
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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The theory of functions of complex variable yields a deeper view to elementary and special functions and gives powerful tools to calculus. Following the contents of Mathematical Analysis III and IV, the theory of curve integral and power series are further developed, conformal mapping is studied and Laplace transform is introduced.
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Prerequisites
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Teaching in English is meant only for erasmus and foreign students. In the case of a small number of students is teaching in a form of individual consultations.
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Assessment methods and criteria
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unspecified
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Recommended literature
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Kopáček, J. Matematika pro fyziky IV, Matfyzpress, Praha, 2003.
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Rudin, W. Analýza v reálném a komplexním oboru, Academia Praha, 2003.
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Veselý, J. Komplexní analýza, Karolinum, Praha, 2000.
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