Subjects(version: 953)
Course, academic year 2023/2024
Calculus 3 - NMMA211
Title: Kalkulus 3 Department of Mathematical Analysis (32-KMA) Faculty of Mathematics and Physics from 2020 winter 8 winter s.:4/2, C+Ex [HT] unlimited unlimited no no not taught Czech full-time full-time
Class: M Bc. FMM Bc. FM > PovinnéM Bc. FM > 2. ročník Mathematics > Real and Complex Analysis {At least one 1st year Calculus course} NMAA073 NMAA073, NMMA221 NMMA341, NMMA212 NMAA073
 Annotation - ---CzechEnglish
The third part of a four-semester course in calculus for bachelor's program Financial Mathematics.
Last update: G_M (16.05.2012)
 Course completion requirements - ---CzechEnglish

Conditions for semester 2019/20

Elaboration of all Sandboxes and Tracks is a necessary condition for the course completion

Detailed explained here:

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

Last update: Pyrih Pavel, doc. RNDr., CSc. (28.10.2019)
 Literature - ---CzechEnglish

J. Kopáček: Matematika pro fyziky III, IV

S. Fučík, J. Milota: Matematická analýza II

Last update: Pyrih Pavel, doc. RNDr., CSc. (28.10.2019)
 Teaching methods - ---CzechEnglish

see

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

Last update: Pyrih Pavel, doc. RNDr., CSc. (28.10.2019)
 Requirements to the exam - ---CzechEnglish

see Course completion requirements

Last update: Pyrih Pavel, doc. RNDr., CSc. (28.10.2019)
 Syllabus - ---CzechEnglish
Multiple integrals.

Basic properties, Fubini theorem, substitutions, polar and spherical

coordinates, volumes.

Measure theory.

basic properties of measure, construction of measure from outer measure,

measurable functions, integral based on measure, Jordan and Lebesgue measures.

Function sequences and series.

Pointwise and uniform convergence (Weierstrass test), commutation of convergence

and limits, derivatives and integrals. Power series and their convergence

radius, derivatives and integrals.

Integrals with parameters.

Commutation of integral with limits, series and derivatives, Gamma and Beta

functions, application to more complicated integrals.

Fourier series.

Trigonometric series, Fourier coeficients, Parseval equation, convergence of

Fourier series, application to series of numbers.

Last update: G_M (27.04.2012)
 Entry requirements - ---CzechEnglish

Previous knowledge of Kalkulus 1 and 2 will be useful.

Last update: Pyrih Pavel, doc. RNDr., CSc. (28.10.2019)

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