SubjectsSubjects(version: 861)
Course, academic year 2019/2020
  
Mathematical Analysis 2 - NMMA102
Title: Matematická analýza 2
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: summer
E-Credits: 10
Hours per week, examination: summer s.:4/4 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: doc. RNDr. Miroslav Zelený, 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
XP//In complex pre-requisite: NMAG204, NMAG211, NMAG212, NMFM204, NMFM205, NMMA201, NMMA202, NMMA203, NMMA204, NMMA205, NMNM201, NMSA336
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: doc. RNDr. Miroslav Zelený, Ph.D. (14.02.2020)

Seminars

Attendance at seminars: at least 50%.

Tests: three passed tests from three, one failed test can be repeated at the end of the semestr; each test consists of three problems;

one has to receive at least 20 points from 30 to pass the test.

This condition excludes repetition.

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Final exam

The exam consists of a written part and an oral part. The details are available at the web page of the lecturer.

Literature -
Last update: doc. RNDr. Miroslav Zelený, Ph.D. (19.02.2020)
BASIC LITERATURE

Lecture notes.

V. Jarník: Diferenciální počet I, Academia 1974.

V. Jarník: Integrální počet I a II, Academia 1984.

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

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

COMPLEMENTARY READING

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

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.

 
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