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Mathematical Analysis 3 - NMAX056

Title:	Matematická analýza 3
Guaranteed by:	Student Affairs Department (32-STUD)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2020
Semester:	summer
E-Credits:	6
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Is provided by:	NMAI056
Additional information:	http://kam.mff.cuni.cz/~klazar/MAIII17.html

Guarantor:	doc. RNDr. Martin Klazar, Dr. doc. Mgr. Robert Šámal, Ph.D.
Class:	Informatika Bc.
Classification:	Mathematics > Real and Complex Analysis
Pre-requisite :	{NXXX014, NXXX015, NXXX016, NXXX017, NXXX018, NXXX022, NXXX023, NXXX024, NXXX025, NXXX033}
Co-requisite :	NMAI054
Incompatibility :	NMAI056
Interchangeability :	NMAI056
Is incompatible with:	NMAI056
Is interchangeable with:	NMAI056

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

Last update: doc. RNDr. Pavel Töpfer, CSc. (26.01.2018)

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.

Course completion requirements -

Last update: doc. RNDr. Pavel Töpfer, CSc. (26.01.2018)

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.

Literature -

Last update: doc. RNDr. Pavel Töpfer, CSc. (26.01.2018)

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.

Requirements to the exam -

Last update: doc. 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: doc. RNDr. Pavel Töpfer, CSc. (26.01.2018)

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.