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The third part of the mathematical analysis course for students of computer science. It explains more advanced
areas with an emphasis on parts useful for computer science.
It will be assumed that the students understand
material covered by Mathematical Analysis 1 and 2.
Last update: Töpfer Pavel, doc. RNDr., CSc. (26.01.2018)
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TThe credit will be given for active participation in tutorials, homeworks and successful completion of tests (the exact weight of each of these criteria is determined by the TA). The nature of the first two requirements does not make it possible for repeated attempts for the credit. The teacher can, however, determine alternative conditions for replacing the missing requirements.
The exam will be written or oral. Obtaining the credit is necessary before the final exam. Last update: Töpfer Pavel, doc. RNDr., CSc. (26.01.2018)
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I. Netuka, Zaklady moderni analyzy, MATFYZPRESS, Praha, 2014 W. Rudin, Analyza v realnem a komplexnim oboru, Academia, Praha, 2003
Sbírky příkladů:
J.Čerych a kol., Příklady z matematické analýzy V (skriptum), SPN, Praha, 1983. B. P. Děmidovič, Sbírka úloh a cvičení z matematické analýzy, Fragment, Praha, 2003. L.Zajíček, Vybrané úlohy z matematické analýzy pro 1. a 2. ročník, Matfyzpress, Praha, 2000. Last update: Töpfer Pavel, doc. RNDr., CSc. (26.01.2018)
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The exam is oral. Before, the student has to already have the "zapocet" from his tutorial. The definitions and facts indicated in the syllabus, more in detail in the scriptum, are required with possible exceptions. Required proofs will be specified. Last update: Honzík Petr, doc. Mgr., Ph.D. (17.09.2018)
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Metric spaces: completeness, connectivity, compactness.
Series: series of real/complex numbers, power series and series of functions. Different types of convergence, operations with series. Fourier series.
Complex analysis: holomorphic functions, Cauchy formula - poles of a function, applications.
Introduction to differential equations: equations with separated variables, linear equations. Existence of a solution, numerical view. Last update: Töpfer Pavel, doc. RNDr., CSc. (26.01.2018)
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