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Lecturer(s)
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Vodák Rostislav, doc. RNDr. Ph.D.
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Ludvík Pavel, RNDr. Ph.D.
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Course content
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1. Complex numbers and their various expressions 2. Basic functions 3. Analytic functions and their properties 4. Integrals of complex functions and primitive functions 5. Line integrals of complex functions 6. The Taylor a Laurent series 7. Singularities, residue and the residue theorem 8. Applications (The Fourier transform, the Schrödinger equations, primitive functions atd.)
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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Understand the mathematical tools of differential and integral calculus of functions of a complex variable and their applications.
Comprehension Understand the mathematical tools of differential and integral calculus of functions of a complex variable.
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Prerequisites
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Understanding the basic elements of mathematical analysis including the mathematical tools of differential and integral calculus.
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Assessment methods and criteria
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unspecified
Credit: the student has to pass one written tests (i.e. to obtain at least half of the possible points). Exam: the student has to understand the subject and be able to prove all theorems.
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Recommended literature
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Brown, J. W., Churchill, R. V. (2013). Complex Variables and Applications, 9 edition. , McGraw-Hill Education.
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Černý, I. (1983). Analýza v komplexním oboru. Academia, Praha.
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Feynman, R. P. (2013). Přednášky z fyziky 1-3. Fragment Praha.
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Marsden, J. E., Hoffman, M. J. (1998). Basic Complex Analysis, Third Edition. W. H. Freeman.
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Needham, T. (1999). Visual Complex Analysis. Clarendon Press.
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Stein, E. M., Shakarchi, R.:. (2003). Complex analysis. , Princeton University Press.
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