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Course, academic year 2024/2025
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Mathematical Analysis I - NMAF033
Title: Matematická analýza I
Guaranteed by: Laboratory of General Physics Education (32-KVOF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: winter
E-Credits: 8
Hours per week, examination: winter s.:4/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Class: Fyzika
Classification: Physics > Mathematics for Physicists
Interchangeability : NMAF051
Is incompatible with: NMAA007, NMAA001, NMAI008, NMAA008, NMAA071, NMAI046, NMAA171
Is pre-requisite for: NMAF003
Is interchangeable with: NMAA001, NMAA171, NMAI008, NMAI046
Annotation -
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.
Last update: G_M (03.06.2004)
Aim of the course -

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.

Last update: T_KVOF (28.03.2008)
Literature - Czech

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)

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

přednáška + cvičení

Last update: T_KVOF (28.03.2008)
Syllabus -

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.

Last update: G_M (03.06.2004)
 
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