SubjectsSubjects(version: 861)
Course, academic year 2019/2020
  
Calculus 3 - NMMA211
Title: Kalkulus 3
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: winter
E-Credits: 8
Hours per week, examination: winter s.:4/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
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
K//Is co-requisite for: NMMA212
P//Is pre-requisite for: NMFM202
Annotation -
Last update: G_M (16.05.2012)
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. (28.10.2019)

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

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

J. Kopáček: Matematika pro fyziky III, IV

S. Fučík, J. Milota: Matematická analýza II

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

see

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

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

see Course completion requirements

Syllabus -
Last update: G_M (27.04.2012)
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.

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

Previous knowledge of Kalkulus 1 and 2 will be useful.

 
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