Mathematical Analysis 2 - NMMA102
Title: Matematická analýza 2
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: summer
E-Credits: 10
Hours per week, examination: summer s.:4/4, 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: prof. RNDr. Stanislav Hencl, Ph.D.
Class: M Bc. MMIB
M Bc. MMIB > Povinné
M Bc. MMIB > 1. ročník
M Bc. MMIT
M Bc. MMIT > Povinné
M Bc. OM
M Bc. OM > Povinné
M Bc. OM > 1. ročník
Classification: Mathematics > Real and Complex Analysis
Co-requisite : NMMA101
Incompatibility : NMAA002
Interchangeability : NMAA002
Is pre-requisite for: NMMA261, NMMA301, NMMA263
Is interchangeable with: NMAA002
In complex pre-requisite: NMAG204, NMAG211, NMAG212, NMFM204, NMFM205, NMMA201, NMMA202, NMMA203, NMMA204, NMMA205, NMNM201, NMSA336
Is complex co-requisite for: NMSA211
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Annotation -
Last update: G_M (16.05.2012)
The second part of a four-semester course in mathematical analysis for bachelor's programs General Mathematics and Information Security.
Course completion requirements -
Last update: prof. RNDr. Luboš Pick, CSc., DSc. (23.12.2022)

see website of the lecturer
Literature -
Last update: prof. RNDr. Luboš Pick, CSc., DSc. (23.12.2022)

Basic sources

lecture notes

V. Jarník: Diferenciální počet I, Academia 1984

V. Jarník: Diferenciální počet II, Academia 1984

B. P. Děmidovič: Sbírka úloh a cvičení z matematické analýzy, Fragment 2003

J. Milota: Matematická analýza I, 1. a 2. část (skriptum), MFF UK 1978

L. Zajíček: Vybrané úlohy z matematické analýzy pro 1. a 2. ročník, Matfyzpress 2006

Supplementary sources

J. Čerych a kol.: Příklady z matematické analýzy V (skriptum), MFF UK 1983

P. Holický, O. Kalenda: Metody řešení vybraných úloh z matematické analýzy pro 2.-4. semestr, Matfyzpress 2006

J. Lukeš a kol.: Problémy z matematické analýzy (skriptum), MFF UK 1982

I. Netuka, J. Veselý: Příklady z matematické analýzy III (skriptum), MFF UK 1977

W. Rudin: Principles of mathematical analysis, McGraw-Hill 1976

Teaching methods - Czech
Last update: prof. RNDr. Luboš Pick, CSc., DSc. (23.12.2022)

Přednáška i cvičení probíhají presenčně. Přednášky nebudou nahrávány ani streamovány.
Syllabus -
Last update: doc. RNDr. Miroslav Zelený, Ph.D. (19.02.2020)
Series

(a) Convergence, divergence, necessary condition of convergence, harmonic series.

(b) Criteria of convergence.

(c) Riemann theorem.

(d) Cauchy product, Mertens theorem.

(e) Complex series.

Integral.

(a) Basic properties of antiderivatives, substitution theorem, Darboux property of derivative, integration by parts.

(b) Integration of rational functions.

(c) Riemann integral.

(d) Newton integral.

(e) Convergence of Newton integral.

(f) Applications of integral.

Ordinary differential equations

(a) Differential equations with separated variables.

(b) Linear differential equations of the first order.

(c) Lineární differential equations of n-th order with constant coefficients.

(d) Systems of differential equations: Peano theorem, Picard theorem.

(e) Systems of linear differential equations.