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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 2025
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

Guarantor:	doc. RNDr. Pavel Pyrih, CSc.
Teacher(s):	prof. RNDr. Miroslav Hušek, DrSc. 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 -

Information available on pages

https://matematika.cuni.cz/pyrih-kalkulus.html

Last update: Pyrih Pavel, doc. RNDr., CSc. (16.09.2025)

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

Last update: Pyrih Pavel, doc. RNDr., CSc. (16.09.2025)

Teaching methods -

see

https://matematika.cuni.cz/pyrih-kalkulus.html

Last update: Pyrih Pavel, doc. RNDr., CSc. (16.09.2025)

Requirements to the exam -

Information available on pages

https://matematika.cuni.cz/pyrih-kalkulus.html

Last update: Pyrih Pavel, doc. RNDr., CSc. (16.09.2025)

Syllabus -

1. ODE

(a) 1st order (Separated variables, homogeneous, kinear, applications)

(b) 2nd order (Linear, constant coefficients)

2. Sequences and series of functions

(a) uniform convergence of series of functions

(b) power series

3. Measure and integral

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

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

(d) Gamma function and Beta function.

(e) Lebesgue-Stieltjes integral.

Last update: Pyrih Pavel, doc. RNDr., CSc. (10.03.2025)

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)