SubjectsSubjects(version: 807)
Course, academic year 2017/2018
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Mathematical Analysis III - NMAI056
Czech title: Matematická analýza III
Guaranteed by: Department of Applied Mathematics (32-KAM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
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
Additional information: http://kam.mff.cuni.cz/~klazar/MAIII17.html
Guarantor: doc. RNDr. Martin Klazar, Dr.
prof. RNDr. Aleš Pultr, DrSc.
Class: Informatika Bc.
Classification: Mathematics > Real and Complex Analysis
Co-requisite : NMAI054
Annotation -
Last update: T_KAM (11.05.2009)

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.
Terms of passing the course -
Last update: doc. RNDr. Martin Klazar, Dr. (12.10.2017)

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

concrete requirements see the page of the teacher of the tutorial

(https://sites.google.com/site/matassileikis/).

No additional terms for obtaining "zápočet" are available.

Literature -
Last update: prof. RNDr. Aleš Pultr, DrSc. (11.10.2017)

Scriptum "Analysis course for computer scientists", see the web page of the Department/Pultr.

Requirements to the exam -
Last update: prof. RNDr. Aleš Pultr, DrSc. (11.10.2017)

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: prof. RNDr. Aleš Pultr, DrSc. (11.10.2017)

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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