Functions of One Complex Variable and Integral Transforms
BASIC DATA
course listing
A - main register
course code
YMX0340
course title in Estonian
Kompleksmuutuja funktsioonid ja funktsionaalteisendused
course title in English
Functions of One Complex Variable and Integral Transforms
course volume CP
-
ECTS credits
6.00
to be declared
yes
fully online course
not
assessment form
Examination
teaching semester
autumn
language of instruction
Estonian
English
Prerequisite(s)
Prerequisite 1
Mathematical Analysis I (YMX0231)Study programmes that contain the course
code of the study programme version
course compulsory
no
Structural units teaching the course
LT - Department of Cybernetics
Timetable link
Version:
VERSION SPECIFIC DATA
course aims in Estonian
Aine eesmärk on anda põhiteadmised kompleksmuutuja funktsiooniteooriast ja rakendustes kasutatavatest funktsionaalteisendustest (z-teisendus, Fourier’ teisendus, Laplace’i teisendus).
course aims in English
The aim of this course is to give basic knowledge of functions of one complex variable and its applications (z-transform, Fourier’ transform, Laplace transform).
learning outcomes in the course in Est.
Õppeaine läbinud üliõpilane on omandanud põhiteadmised kompleksmuutuja funktsiooniteooriast ja põhilistest funktsionaalteisendustest ning rakendab neid praktiliste ülesannete lahendamisel:
- valdab matemaatilist baasi;
- rakendab resiide integraalide arvutamisel;
- kasutab Laplace’i teisendust diferentsiaalvõrrandite lahendamisel ja konvolutsiooni arvutamisel;
- kasutab iseseisvalt matemaatilisi meetodeid erialaste probleemide lahendamiseks.
- valdab matemaatilist baasi;
- rakendab resiide integraalide arvutamisel;
- kasutab Laplace’i teisendust diferentsiaalvõrrandite lahendamisel ja konvolutsiooni arvutamisel;
- kasutab iseseisvalt matemaatilisi meetodeid erialaste probleemide lahendamiseks.
learning outcomes in the course in Eng.
After completing this course, the student has basic knowledge of complex analysis and can apply this knowledge to solve practical problems:
- has basic knowledge in complex analysis;
- applies residue calculus to evaluate integrals in the real line;
- applies Laplace transform to solve differential equations and in evaluation of convolution of two functions;
- independently uses mathematical methods in solving engineering problems.
- has basic knowledge in complex analysis;
- applies residue calculus to evaluate integrals in the real line;
- applies Laplace transform to solve differential equations and in evaluation of convolution of two functions;
- independently uses mathematical methods in solving engineering problems.
brief description of the course in Estonian
1. Kompleksarvud ja kompleksmuutuja funktsioonid, kiire Fourier’ teisendus.
2. Analüütilised funktsioonid, harmoonilised funktsioonid ja integraal,
3. Funktsionaalread, Laurent’i rida ja z-teisendus.
4. Resiidid ja nende rakendused.
5. Laplace’i ja Fourier’ teisendus.
2. Analüütilised funktsioonid, harmoonilised funktsioonid ja integraal,
3. Funktsionaalread, Laurent’i rida ja z-teisendus.
4. Resiidid ja nende rakendused.
5. Laplace’i ja Fourier’ teisendus.
brief description of the course in English
1. Complex numbers and functions of one complex variable, fast Fourier’ transform.
2. Analytic functions, harmonic functions and integration in the complex plane.
3. Functional series, Laurent series and z-transform.
4. Residues and their applications.
5. Laplace’ and Fourier’ transforms.
2. Analytic functions, harmonic functions and integration in the complex plane.
3. Functional series, Laurent series and z-transform.
4. Residues and their applications.
5. Laplace’ and Fourier’ transforms.
type of assessment in Estonian
-
type of assessment in English
-
independent study in Estonian
-
independent study in English
-
study literature
Alar Leibak, Kompleksmuutuja funktsioonid, TTÜ Kirjastus, 2015
Endel Jürimäe, Kompleksmuutuja funktsioonide teooria lühikursus, Tln. “Valgus”, 1983
Peter Henrici, Applied and computational complex analysis. / Vol. 1, Power series, integration, conformal mapping, location of zeros, Wiley, 1988
Peter Henrici, Applied and computational complex analysis. / Vol.2, Special functions, integral transforms, asymptotics, continued fractions, Wiley, 1991
Peter Henrici, Applied and computational complex analysis. / Vol. 3, Discrete fourier analysis, Cauchy integrals, construction of conformal maps, univalent functions, Wiley, 1993
Aksel Jõgi, Integraalaalteisendused, TTÜ, 2003
Endel Jürimäe, Kompleksmuutuja funktsioonide teooria lühikursus, Tln. “Valgus”, 1983
Peter Henrici, Applied and computational complex analysis. / Vol. 1, Power series, integration, conformal mapping, location of zeros, Wiley, 1988
Peter Henrici, Applied and computational complex analysis. / Vol.2, Special functions, integral transforms, asymptotics, continued fractions, Wiley, 1991
Peter Henrici, Applied and computational complex analysis. / Vol. 3, Discrete fourier analysis, Cauchy integrals, construction of conformal maps, univalent functions, Wiley, 1993
Aksel Jõgi, Integraalaalteisendused, TTÜ, 2003
study forms and load
daytime study: weekly hours
4.0
session-based study work load (in a semester):
lectures
2.0
lectures
-
practices
0.0
practices
-
exercises
2.0
exercises
-
lecturer in charge
Alar Leibak, vanemlektor (LT - küberneetika instituut)
LECTURER SYLLABUS INFO
semester of studies
teaching lecturer / unit
language of instruction
Extended syllabus
2025/2026 autumn
Alar Leibak, LT - Department of Cybernetics
Estonian