457-0047/01 – Functions of Complex Variable (FKP)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantorprof. RNDr. Jiří Bouchala, Ph.D.Subject version guarantorprof. RNDr. Jiří Bouchala, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year2Semestersummer
Study languageCzech
Year of introduction1992/1993Year of cancellation2009/2010
Intended for the facultiesFEIIntended for study typesMaster
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

To supply working knowledge of basic concepts of differential and integral calculus of complex function, together with theory of power and Laurent series. Student should also learn how to apply the theory in solving practical problems.

Teaching methods

Lectures
Tutorials
Project work

Summary

Subject contains principles of calculus of function of complex variable including power and Laurent series and the theory of residua.

Compulsory literature:

I. Černý: Foundations of Analysis in the Complex Domain, Academia, Praha, 1992.

Recommended literature:

J. Bouchala: Funkce komplexní proměnné, www.am.vsb.cz/bouchala. J. Bouchala: Sbírka příkladů z komplexní analýzy, www.am.vsb.cz/bouchala. I. Černý: Základy analysy v komplexním oboru, Academia, Praha, 1967. P. Galajda, Š. Schrötter: Funkcie komplexnej premennej a operátorový počet, Alfa, Bratislava, 1991.

Way of continuous check of knowledge in the course of semester

Podmínky udělení zápočtu: Absolvování testu a vyřešení zadaných domácích úkolů. Hodnocení: ze cvičení lze získat maximálně 30 bodů

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Přednášky: Diferenciální a integrální počet komplexních funkcí komplexní proměnné: komplexní čísla, rozšířená Gaussova rovina; komplexní funkce reálné a komplexní proměnné; derivace komplexní funkce komplexní proměnné; konformní zobrazení; integrál komplexní funkce, Cauchyho vzorce. Posloupnosti a řady komplexních funkcí: mocninné řady, Taylorovy řady; Laurentovy řady, klasifikace singulárních bodů; rezidua, reziduová věta a její aplikace. Cvičení: Řešení úloh na téma: komplexní čísla, rozšířená Gaussova rovina; komplexní funkce reálné a komplexní proměnné; derivace komplexní funkce komplexní proměnné; konformní zobrazení; integrál komplexní funkce, Cauchyho vzorce; mocninné a Taylorovy řady; Laurentovy řady, klasifikace singulárních bodů; rezidua, reziduová věta.

Conditions for subject completion

Conditions for completion are defined only for particular subject version and form of study

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2005/2006 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 2 Compulsory study plan
2005/2006 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 2 Compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 2 Compulsory study plan
2005/2006 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 2 Compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 2 Compulsory study plan
2004/2005 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 2 Compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 2 Compulsory study plan
2004/2005 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 2 Compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 2 Compulsory study plan
2000/2001 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 2 Compulsory study plan
2000/2001 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 2 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner