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Course, academic year 2019/2020
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Mathematical Analysis III - NMAI056
Title in English: Matematická analýza III
Guaranteed by: Department of Applied Mathematics (32-KAM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2019
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: doc. Mgr. Robert Šámal, Ph.D.
Mgr. Petr Honzík, Ph.D.
doc. RNDr. Martin Klazar, Dr.
Class: Informatika Bc.
Classification: Mathematics > Real and Complex Analysis
Co-requisite : NMAI054
Annotation -
Last update: doc. RNDr. Pavel Töpfer, CSc. (26.01.2018)
Continuation of the course in mathematical analysis for students of computer science covering the theory of metric spaces, series of functions and elements of complex analysis.
Course completion requirements -
Last update: Mgr. Petr Honzík, Ph.D. (17.09.2018)

The student has to have completed the associated tutorial with "zápočet". For

concrete requirements see the page of the teacher of the tutorial

No additional terms for obtaining "zápočet" are available. Exam has both written and oral part.

Literature -
Last update: Mgr. Petr Honzík, Ph.D. (17.09.2018)

Jiří Kopáček a kol. Příklady z matematiky pro fyziky (IV)

List of definitions and theorems on the homepage of the teacher

Requirements to the exam -
Last update: Mgr. Petr Honzík, Ph.D. (17.09.2018)

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.

Syllabus -
Last update: Mgr. Petr Honzík, Ph.D. (17.09.2018)

Metric spaces (separability, completeness, compactness, Heine-Borel theorem).

Series of functions (uniform convergence, properties of uniform convergence, power series, Fourier series).

Elements of complex analysis (power series in complex domain, derivative, Cauchy-Riemann equations, integral, Cauchy's theorem, applications).

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