SubjectsSubjects(version: 875)
Course, academic year 2016/2017
  
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 [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: prof. RNDr. Josef Málek, CSc., DSc.
RNDr. Miroslav Bulíček, Ph.D.
Class: Fyzika
Classification: Physics > Mathematics for Physicists
Interchangeability : NMAF033
XP//In complex pre-requisite: NMAG204, NMMA201, NMMA202, NMMA203, NMNM201, NNUM105
Annotation -
Last update: G_F (22.05.2008)
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.
Aim of the course -
Last update: T_KMA (13.05.2008)

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: doc. Mgr. Milan Pokorný, Ph.D. (28.09.2018)
  • 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
Teaching methods - Czech
Last update: doc. Mgr. Milan Pokorný, Ph.D. (28.09.2018)

přednáška + cvičení

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

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.

 
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