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Course, academic year 2023/2024
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Calculus IIa - NMAA073
Title: Kalkulus IIa
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
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: cancelled
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Classification: Mathematics > Real and Complex Analysis
Pre-requisite : {Calculus Ia, Ib}
Incompatibility : NMAA003
Interchangeability : NMMA211
Is incompatible with: NMMA211, NMMA221
Is interchangeable with: NMMA211, NMMA221
Annotation -
Last update: T_KMA (13.09.2010)
Calculus for the second year of Bc. study (3. semester). Topics : multiple integrals, measure theory, integration with parameters, function sequences and series, Fourier series.
Literature - Czech
Last update: T_KMA (23.05.2008)

J. Kopáček: Matematika pro fyziky III, IV

S. Fučík, J. Milota: Matematická analýza II

Syllabus -
Last update: T_KMA (13.09.2010)
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.

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