SubjectsSubjects(version: 970)
Course, academic year 2016/2017
   Login via CAS
Mathematical Analysis I - NMAF051
Title: Matematická analýza I
Guaranteed by: Laboratory of General Physics Education (32-KVOF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2016 to 2016
Semester: winter
E-Credits: 10
Hours per week, examination: winter s.:4/3, 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
Guarantor: prof. RNDr. Josef Málek, CSc., DSc.
doc. RNDr. Miroslav Bulíček, Ph.D.
Teacher(s): doc. RNDr. Marie Běhounková, Ph.D.
doc. RNDr. Miroslav Bulíček, Ph.D.
prof. Ing. Branislav Jurčo, CSc., DSc.
doc. RNDr. Michal Pavelka, Ph.D.
RNDr. Ondřej Šrámek, Ph.D.
doc. RNDr. Dr. rer. nat. Jan Vybíral, Ph.D.
doc. RNDr. Miloš Zahradník, CSc.
Class: Fyzika
Classification: Physics > Mathematics for Physicists
Interchangeability : NMAF033
Is interchangeable with: NMAF033
In complex pre-requisite: NMAG204, NMMA201, NMMA202, NMMA203, NMNM201, NNUM105
Annotation -
First part of the basic course of mathematics for the students of general physics (bachelor study). The program consists of basics on differential and integral calculus, together with theoretical background.
Last update: G_F (22.05.2008)
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_KMA (13.05.2008)
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)
  • Videozáznamy přednášek
Last update: Pokorný Milan, prof. Mgr., Ph.D., DSc. (28.09.2018)
Teaching methods - Czech

přednáška + cvičení

Last update: Pokorný Milan, prof. Mgr., Ph.D., DSc. (28.09.2018)
Syllabus -

1. Sets and operations on sets, predicate logic.

2. Sets of numbers. The supremum axiom. Sequences and their limits, accumulations points, countable and non-countable sets. Bolzano-Cauchy Theorem.

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

4. Derivative and differential of a function of one real variable. Arithmetic on derivatives.

5. Primitive function, integration by parts and Theorem on Substitution; integration of elementary functions, especially rational ones. Solution to special ODEs.

6. Properties of continuous functions on a closed interval. , 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), Taylor polynomial and Taylor formula.

7. Definite (Riemann, Newton) 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, moments.

Last update: Pokorný Milan, prof. Mgr., Ph.D., DSc. (28.09.2018)
 
Charles University | Information system of Charles University | http://www.cuni.cz/UKEN-329.html