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Lecturer(s)
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Staněk Svatoslav, prof. RNDr. CSc.
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Tomeček Jan, doc. RNDr. Ph.D.
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Course content
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Differential calculus in normed linear spaces. Frechet and Gateaux derivative. Theorem on implicit operator. Theorems on extreme values of functionals. Measure theory. Absolutely continuous functions. Lebesgue, Stieltjes and Bochner integral. Integral of complex variable function. Residue theory. Meromorphic functions. Zeros of holomorphic functions. Analytic continuation.
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Learning activities and teaching methods
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Dialogic Lecture (Discussion, Dialog, Brainstorming), Work with Text (with Book, Textbook)
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Learning outcomes
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Understand of differential calculus in normed linear spaces the measure theory and integrals and the mathematical tools of differential and integral calculus of functions of complex variable.
Comprehension Understand of differential calculus in normed linear spaces the measure theory and integrals and the mathematical tools of differential and integral calculus of functions of complex variable.
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Prerequisites
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Master's degree in mathematics.
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Assessment methods and criteria
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Oral exam
Exam: to know and to understand the subject
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Recommended literature
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I. Černý. (1983). Analýza v komplexním oboru. Academia Praha.
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J. Lukeš, J. Malý. (1993). Míra a integrál. UK Praha.
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J. Lukeš. (1972). Teorie míry a nitegrálu. SPN Praha.
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R.G. Bartle. (2001). A modern theory of integration. AMS Providence, Rhode Island.
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S. Fučík, J. Milota. (1975). Matematická analýza II. SPN Praha.
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S. Fučík, O. John, A. Kufner. (1974). Prostory funkcí I. SPN Praha.
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S. Lang. (1993). Real and functional analysis. Springer.
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S.Lang. (2001). Complex Analysis. Springer, Berlin.
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W. Rudin. (1977). Analýza v reálném a komplexním oboru. Academia Praha.
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