Subjects

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Calculus 3 - NMMA211

Title:	Kalkulus 3
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2020
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:	not taught
Language:	Czech
Teaching methods:	full-time

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, NMMA221
Is co-requisite for:	NMMA341, NMMA212
Is interchangeable with:	NMAA073

Annotation -

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 -

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 -

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 -

see

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

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

Requirements to the exam -

see Course completion requirements

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

Syllabus -

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 -

Previous knowledge of Kalkulus 1 and 2 will be useful.

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