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Mathematical analysis IV - NMTM202

Title:	Matematická analýza IV
Guaranteed by:	Department of Mathematics Education (32-KDM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2022
Semester:	summer
E-Credits:	4
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

Guarantor:	RNDr. Martin Rmoutil, Ph.D. RNDr. Jakub Staněk, Ph.D.
Incompatibility :	NMUM202
Interchangeability :	NMUM202
Is incompatible with:	NMUM202
Is interchangeable with:	NMUM202

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

Last update: RNDr. Jakub Staněk, Ph.D. (14.06.2019)

Basic course in mathematical analysis for second year students.

Course completion requirements -

Last update: RNDr. Martin Rmoutil, Ph.D. (25.02.2021)

To successfully pass the subject, it is necessary to obtain credit ("zapocet") and pass the examination. Obtaining "zapocet" is a necessary condition for signing into an examination.

Credit will be granted if, and only if, the student correctly solves all the problems from designated problem sets distributed by the lecturer during the term. The last set will be sent sufficiently in advance before the beginning of the examination period.

The student solves the problems and sends his solutions to the lecturer who, in turn, provides feedback to the student. In case of faulty solutions, the student needs to repeat the first step until his or her solutions are correct.

Literature -

Last update: RNDr. Jakub Staněk, Ph.D. (14.06.2019)

Kopáček, J. Matematická analýza nejen pro fyziky II. Matfyzpress, Praha, 2007.

Kopáček, J. Příklady z matematiky nejen pro fyziky II. Matfyzpress, Praha, 2006.

Veselý, J. Základy matematické analýzy I. Matfyzpress, Praha, 2004.

Veselý, J. Základy matematické analýzy II. Matfyzpress, Praha, 2009.

Došlá, Z. a kol. Diferenciální počet funkcí více proměnných s programem Maple V. Brno, 1999. Dostupné z < http://www.math.muni.cz/~plch/mapm/index_cd.html>.

Černý, I. Úvod do inteligentního kalkulu 2. Academia, Praha, 2005.

Brabec, J., Hrůza, B. Matematická analýza II. SNTL/Alfa, Praha, 1986.

Trench, W. F. Introduction to Real Analysis. Dostupné z < http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF >

Hairer, E., Wanner, G. Analysis by its History. Springer, 2008.

Requirements to the exam -

Last update: RNDr. Martin Rmoutil, Ph.D. (25.02.2021)

The subject is finished by passing an exam. Depending on the epidemic situation, the exam may take two forms: either it will be a written exam followed possibly by an oral complement, or it will be an online oral exam using Zoom. It can also happen that both approaches will need to be combined, in which case the examinator (i.e. the lecturer) will be extra careful to level the difficulty levels of both methods.

Further information in English will be provided by the lecturer upon request. Any such requests should kindly be sent to rmoutil[at]karlin.mff.cuni.cz.

Syllabus -

Last update: RNDr. Martin Rmoutil, Ph.D. (25.02.2021)

Uniform konvergence of sequences and series interchange of limits, commutativity of limits with derivatives. Power series in complex domain.

Taylor series, diferentiation and integration of power series, domains of convergence.

Metric spaces.

Functions of several variables, limits and continuity. Partial derivatives, total derivative, gradient. Local and constrained extrema.