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Course, academic year 2023/2024
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Calculus 2 - NMMA221
Title: Kalkulus 2
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023 to 2023
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: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. RNDr. Pavel Pyrih, CSc.
Class: M Bc. FM
M Bc. FM > Povinné
M Bc. FM > 2. ročník
Classification: Mathematics > Real and Complex Analysis
Pre-requisite : {At least one 1st year Calculus course}
Incompatibility : NMAA073
Interchangeability : NMAA073
Is pre-requisite for: NMMA341, NMFM202
Is interchangeable with: NMMA211
Annotation -
The third part of a four-semester course in calculus for bachelor's program Financial Mathematics.
Last update: Kaplický Petr, doc. Mgr., Ph.D. (30.05.2019)
Course completion requirements -


The exact conditions for granting credit are determined by the trainee.

Earning credit is a condition for taking the exam.

More detailed information can be found on the lecturer's page:


Credit will be awarded after the elaboration of tasks (see the link below).

Gaining credit is a condition for taking the exam.

The form of the exam will be full-time or distance and will always be specified in the SIS for individual dates.

The full-time form of the exam will take place as in previous semesters (see the link below).

The distance form of the exam will take place in the Zoom environment and will be a modification of the full-time form.

Everything is described in more detail on the page

Last update: Pyrih Pavel, doc. RNDr., CSc. (19.09.2023)
Literature -

O. Hájková, M. Johanis, O. John, O. Kalenda, M. Zelený: Matematika

J. Lukeš, J. Malý: Míra a integrál (Measure and integral)

P. Holický, O. Kalenda: Metody řešení vybraných úloh z matematické analýzy pro 2. - 4. semestr

J. Lukeš: Příklady k teorii Lebesgueova integrálu

V. Jarník: Diferenciální počet I, II

Next resources

Last update: Pyrih Pavel, doc. RNDr., CSc. (14.09.2021)
Teaching methods -


Last update: Pyrih Pavel, doc. RNDr., CSc. (14.09.2021)
Requirements to the exam -

see Course completion requirements

Last update: Pyrih Pavel, doc. RNDr., CSc. (14.09.2021)
Syllabus -

Functions of several variables II (implicit function theorem, free and bounded extrema).

Sequences and series of functions (uniform convergence of series of functions, power series).

Introduction to measure theory (measurable representations, abstract Lebesgue integral, Lebesgue measure on R ^ n).

Multidimensional integral (Fubini's theorem, Substitution theorem, contents of shapes and volumes of bodies).

Swap integral order and limits, integral and series, or integral and derivative.

Gamma function and Beta function.

Lebesgue-Stieltjes integral.

Last update: Pyrih Pavel, doc. RNDr., CSc. (14.09.2021)
Entry requirements -

To understand the material, it is suitable if the student has already completed the course Calculus 1.

Last update: Pyrih Pavel, doc. RNDr., CSc. (14.09.2021)
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