Course detail

Othogonal systems of the special functions.

FEKT-SOSFAcad. year: 2005/2006

Gamma and Beta functions, cylindric functions,Bessel dif. equation, Fourier-Bessel series, oscillation of circular membrane, lateral zone of frequency modulated wave, orthogonal polynomials.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

RNDr. Svatopluk Švarc, CSc.

Department

Department of Mathematics (UMAT)

Learning outcomes of the course unit

Not applicable.

Prerequisites

It is a course of the non-structured ending study program

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

A goal is to apply special functions, as Gamma, Beta,
cylindric functions and orthogonal polynomials for solving some differential equations of 2. order, boundary problems for partial dif. equations through Bessel-Fourier series (equation of membrane oscillation) and for frequency modulation.

Specification of controlled education, way of implementation and compensation for absences

Not applicable.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

KORENĚV B.G.:Úvod do teorie Besselových funkcí,SNTL Praha 1971
BATEMAN ERDELYI:Higher Transcendental Functions,MC GRAW-HILL BOOK COMPANY NEW YORK TORONTO LONDON 1953
KUZNĚCOV D.S.:Specialnyje funkcii,Moskva 1965

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme EI-B3 Bachelor's

    branch B3-KAM , 3. year of study, summer semester, optional interdisciplinary
    branch B3-EST , 3. year of study, summer semester, optional interdisciplinary
    branch B3-SEE , 3. year of study, summer semester, optional interdisciplinary
    branch B3-EVM , 3. year of study, summer semester, optional interdisciplinary

  • Programme EI-M5 Master's

    branch M5-KAM , 3. year of study, summer semester, optional interdisciplinary

  • Programme EI-M5 Master's

    branch M5-KAM , 3. year of study, summer semester, optional interdisciplinary

  • Programme EI-M5 Master's

    branch M5-EST , 3. year of study, summer semester, optional interdisciplinary

  • Programme EI-M5 Master's

    branch M5-EST , 3. year of study, summer semester, optional interdisciplinary
    branch M5-SEE , 3. year of study, summer semester, optional interdisciplinary

  • Programme EI-M5 Master's

    branch M5-SEE , 3. year of study, summer semester, optional interdisciplinary

  • Programme EI-M5 Master's

    branch M5-EVM , 3. year of study, summer semester, optional interdisciplinary

  • Programme EI-M5 Master's

    branch M5-EVM , 3. year of study, summer semester, optional interdisciplinary

  • Programme EI-M5 Master's

    branch M5-KAM , 4. year of study, summer semester, optional interdisciplinary

  • Programme EI-M5 Master's

    branch M5-KAM , 4. year of study, summer semester, optional interdisciplinary
    branch M5-EST , 4. year of study, summer semester, optional interdisciplinary

  • Programme EI-M5 Master's

    branch M5-EST , 4. year of study, summer semester, optional interdisciplinary
    branch M5-SEE , 4. year of study, summer semester, optional interdisciplinary

  • Programme EI-M5 Master's

    branch M5-SEE , 4. year of study, summer semester, optional interdisciplinary

  • Programme EI-M5 Master's

    branch M5-EVM , 4. year of study, summer semester, optional interdisciplinary

  • Programme EI-M5 Master's

    branch M5-EVM , 4. year of study, summer semester, optional interdisciplinary
    branch M5-KAM , 5. year of study, summer semester, optional interdisciplinary

  • Programme EI-M5 Master's

    branch M5-KAM , 5. year of study, summer semester, optional interdisciplinary

  • Programme EI-M5 Master's

    branch M5-EST , 5. year of study, summer semester, optional interdisciplinary

  • Programme EI-M5 Master's

    branch M5-EST , 5. year of study, summer semester, optional interdisciplinary

  • Programme EI-M5 Master's

    branch M5-SEE , 5. year of study, summer semester, optional interdisciplinary

  • Programme EI-M5 Master's

    branch M5-SEE , 5. year of study, summer semester, optional interdisciplinary

  • Programme EI-M5 Master's

    branch M5-EVM , 5. year of study, summer semester, optional interdisciplinary

  • Programme EI-M5 Master's

    branch M5-EVM , 5. year of study, summer semester, optional interdisciplinary

  • Programme EI-M3 Master's

    branch M3-KAM , 1. year of study, summer semester, optional interdisciplinary
    branch M3-EST , 1. year of study, summer semester, optional interdisciplinary
    branch M3-SEE , 1. year of study, summer semester, optional interdisciplinary
    branch M3-EVM , 1. year of study, summer semester, optional interdisciplinary
    branch M3-KAM , 2. year of study, summer semester, optional interdisciplinary
    branch M3-EST , 2. year of study, summer semester, optional interdisciplinary
    branch M3-SEE , 2. year of study, summer semester, optional interdisciplinary
    branch M3-EVM , 2. year of study, summer semester, optional interdisciplinary
    branch M3-KAM , 3. year of study, summer semester, optional interdisciplinary
    branch M3-EST , 3. year of study, summer semester, optional interdisciplinary
    branch M3-SEE , 3. year of study, summer semester, optional interdisciplinary
    branch M3-EVM , 3. year of study, summer semester, optional interdisciplinary

Type of course unit

 

Lecture

28 hours, optionally

Teacher / Lecturer

RNDr. Svatopluk Švarc, CSc.

Syllabus

A calculation of improper integrals by using Gamma and Beta functions, complementary formulae, Stirling formula.
An expression of Gamma function through infinite products.
Relations between Gamma and Beta functions.
Bessel differential equation.
Bessel and Neumann functions, recurrent and derivative formulae.
Zeros of cylindric functions.
Bessel functions with "half-integer" indices.
Orthogonality of Bessel functions, Fourier-Bessel series.
Oscillation of circular membrane.
Lateral zone of frequency modulated wave.
Hankel functions, modified cylindric functions.
Differential equations transformable to a Bessel one.
Czebyshew, Laguerre and Legendre polynomials.
Differential equations of orthogonal polynomials.

Fundamentals seminar

28 hours, optionally

Teacher / Lecturer

RNDr. Svatopluk Švarc, CSc.

Syllabus

Solving problems with connection to a lectrure.