Subjects(version: 945)
Mathematical Analysis I - NMAF033
Title: Matematická analýza I Laboratory of General Physics Education (32-KVOF) Faculty of Mathematics and Physics from 2022 winter 8 winter s.:4/2, C+Ex [HT] unlimited unlimited no no cancelled Czech full-time full-time
Class: Fyzika Physics > Mathematics for Physicists NMAF051 NMAA007, NMAA001, NMAI008, NMAA008, NMAA071, NMAI046, NMAA171 NMAF003 NMAA001, NMAA171, NMAI008, NMAI046
 Annotation - ---CzechEnglish
Last update: G_M (03.06.2004)
First part of the basic course of mathematics for the students of physics (bachelor study). The program consists of basics on differential and integral calculus, together with theoretical background.
 Aim of the course - ---CzechEnglish
Last update: T_KVOF (28.03.2008)

First part of the basic course of mathematics for the students of physics (bachelor study). The program consists of basics on differential and integral calculus, together with theoretical background.

 Literature - Czech
Last update: RNDr. Pavel Zakouřil, Ph.D. (05.08.2002)

Kopáček J.: Matematika pro fyziky I.,II.,III. Skripta MFF UK

Kopáček J. a kol. : Příklady z matematiky pro fyziky I., II. Skripta MFF UK

Jarník J.: Diferenciální počet I.,II

Jarník J.: Integrální počet I

Děmidovič V.: Sbírka úloh a cvičení z matematické analýzy (rusky)

 Teaching methods - Czech
Last update: T_KVOF (28.03.2008)

přednáška + cvičení

 Syllabus - ---CzechEnglish
Last update: G_M (03.06.2004)

1. Sets and operations on sets, numbers and sets of numbers.

2. The supremum axiom.

3. Sequences and their limits, accumulations points, countable and non-countable sets. Bolzano-Cauchy Theorem, Bolzano-Weierstrass Theorem.

4. Function of one real variable, limit and continuity. Elementary functions. One-to-one function. composite function, parametrically given function.

5. Properties of continuous functions on a closed interval.

6. Derivative and differential of a function of one real variable. Theorem on the increase of a function, Mean Value Theorem. Sketching of the graph of a function using derivatives. Convexity and concavity. L'Hospital's Rule, symbols o and O (small and capital o).

7. Taylor polynomial and Taylor formula with different forms of the remainder.

8. Primitive function, integration by parts and Theorem on Substitution; integration of elementary functions, especially rational ones.

9. Definite (Riemann) integral. Integral with changing upper limit. Connection between primitive function and definite integral. Mean Value Theorem of the integral calculus. Applications: lenght of a curve, volume of a rotational body, surface in polar coordinates.

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