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Course, academic year 2023/2024
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Mathematical Analysis 1 - NMMA101
Title: Matematická analýza 1
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023 to 2023
Semester: winter
E-Credits: 10
Hours per week, examination: winter 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
Incompatibility : NMAA001, NMMA111
Interchangeability : NMAA001
Is co-requisite for: NMMA102
Is incompatible with: NMMA111
Is pre-requisite for: NMMA261, NMMA301, NMMA263, NMMA162
Is interchangeable with: NMAA001, NMMA111
In complex pre-requisite: NMAG204, NMAG211, NMAG212, NMFM204, NMFM205, NMMA201, NMMA202, NMMA203, NMMA204, NMMA205, NMNM201, NMSA336
Is complex co-requisite for: NMSA211
Annotation -
The first part of a four-semester course in mathematical analysis for bachelor's programs General Mathematics and Information Security.
Last update: G_M (16.05.2012)
Course completion requirements -

Detailed requirements will be posted on the instructor's personal website.

Last update: Pick Luboš, prof. RNDr., CSc., DSc. (28.09.2022)
Literature -
BASIC LITERATURE

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

COMPLEMENTARY READING

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

Last update: G_M (24.04.2012)
Teaching methods - Czech

Přednáška i cvičení probíhají presenčně. Přednášky nebudou nahrávány ani streamovány.

Last update: Pick Luboš, prof. RNDr., CSc., DSc. (11.10.2022)
Syllabus -
1. Introduction

Logic, mappings, countable sets, real numbers, supremum property, complex numbers.

2. Limit of sequences

Convergence of sequences, the limit of a monotone sequence, values of accumulation, limsup, liminf, Bolzano-Weierstrass theorem, Cantor principle, Bolzano-Cauchy condition.

3. Limit of functions and continuity

Basic notions, limit, the neighborhood of a point, limit and continuity at a point (one-sided versions included), theorems on limits and arithmetics, ordering, the limit of a composed function, Heine theorem, the limit of a monotone function, continuous functions on an interval (intermediate value theorem, continuous image, boundedness, attaining of extrema, continuity of an inverse function.

4. Elementary functions

Exponential, logarithmic, goniometric and cyclometric, and power function (without proofs).

5. Derivative

Definition and basic properties, arithmetics of derivatives, the derivative of a composed function, derivative of an inverse function,

derivative of elementary functions, Rolle theorem, Lagrange theorem, Cauchy theorem, l'Hospital rule, the limit of a derivative at a point, monotonicity and sign of a derivative, convex and concave functions, inflection point, derivative and convexity, asymptote, investigation of a function.

6. Taylor polynomial

Taylor polynomial, Peano theorem, Lagrange theorem, Cauchy theorem, the symbol "little o" and its properties, Taylor polynomial of elementary functions.

Last update: Pick Luboš, prof. RNDr., CSc., DSc. (30.07.2022)
 
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