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Analytic Functions of One Complex Variable

General data

Course ID: 1000-134FAN*
Erasmus code / ISCED: 11.1 The subject classification code consists of three to five digits, where the first three represent the classification of the discipline according to the Discipline code list applicable to the Socrates/Erasmus program, the fourth (usually 0) - possible further specification of discipline information, the fifth - the degree of subject determined based on the year of study for which the subject is intended. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title: Analytic Functions of One Complex Variable
Name in Polish: Funkcje analityczne*
Organizational unit: Faculty of Mathematics, Informatics, and Mechanics
Course groups: Obligatory courses for 3rd grade JSIM (3M+4I)
Obligatory courses for 3rd grade Mathematics
Obligatory courses for 4th grade JSIM (3I+4M)
ECTS credit allocation (and other scores): 6.00 Basic information on ECTS credits allocation principles:
  • the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS;
  • the student’s weekly hourly workload is 45 h;
  • 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes;
  • weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS;
  • work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load.
view allocation of credits
Language: (unknown)
Type of course:

elective courses
Short description:

Basic properties of analytic functions of one complex variable. A beautiful part of analysis with many applications all throughout mathematics.
Full description:

Functions of one complex variable, function series, power series. Complex derivative. Holomorphic functions. Contour integrals. Path-independence of the contour integral from the path vs existence of a primitive function. Cauchy Theorem. Cauchy integral formula. Holomorphic functions vs analytic functions. Morera Theorem. Entire functions and Liouville Theorem. Weierstrass Theorem. The identity principle. Laurent series. The

classification of isolated singular points. Casorati-Weierstrass Theorem. Residue Theorem and its applications. Meromorphic functions. The argument principle. Rouche Theorem. The Multiplicity Theorem and the Open Mapping Theorem. The maximum principle. Schwarz Lemma. Conformal mappings.

Classes in period "Winter semester 2024/25" (past)

Time span: 2024-10-01 - 2025-01-26
Selected timetable range:
Go to timetable
Type of class:
Classes, 30 hours more information
Lecture, 30 hours more information
Coordinators: Piotr Nayar
Group instructors: Maciej Białobrzeski, Piotr Nayar, Marta Strzelecka
Students list: (inaccessible to you)
Credit: Examination
Notes: (in Polish)

Ocena końcowa na podstawie uzyskanego łącznego dorobku punktowego: prace domowe do 100 pkt., kolokwia do 100 pkt. (2x50). Egzamin ustny dla wybranych osób.

Classes in period "Winter semester 2025/26" (future)

Time span: 2025-10-01 - 2026-01-25

Selected timetable range:
Go to timetable
Type of class:
Classes, 30 hours more information
Lecture, 30 hours more information
Coordinators: Piotr Nayar
Group instructors: Piotr Nayar, Marta Strzelecka
Students list: (inaccessible to you)
Credit: Examination
Notes: (in Polish)

Ocena końcowa na podstawie uzyskanego łącznego dorobku punktowego: prace domowe do 100 pkt., kolokwia do 100 pkt. (2x50). Egzamin ustny dla wybranych osób.
Course descriptions are protected by copyright.
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