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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
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

Opinion survey results Examination dates WS schedule Noticeboard

Annotation -

Last update: doc. Mgr. Petr Kaplický, Ph.D. (30.05.2019)

The third part of a four-semester course in calculus for bachelor's program Financial Mathematics.

Course completion requirements -

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

TERMS FOR WINTER SEMESTER 2023/24

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:

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

CONDITIONS FOR SEMESTER 2021/22

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

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

Literature -

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

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

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

Teaching methods -

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

see

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

Requirements to the exam -

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

see Course completion requirements

Syllabus -

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

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.

Entry requirements -

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

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