MATS122 Complex Analysis 2 (5 cr)

Open the course unit brochure on Sisu
Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023

Description

The power series representation of a holomorphic (analytic) function. Cauchy's integral theorem and integral formula for simply connected domains. Laurent expansion. Residue calculus  and elements of conformal mappings, Riemann's mapping theorem. Singular points of analytic functions. (Freitag and Busam: Complex analysis, chapters 3 and 4)

Learning outcomes

After passing the course successfully the student:

  • knows the connection between holomorphic (analytic) functions and power series
  • understands the concepts of the winding number and simply connected domains
  • can derive and apply Cauchy's integral theorem and the residue theorem
  • knows the Laurent series
  • knows basic properties of conformal mappings
  • manages a bit more complicated applications of complex analysis

Description of prerequisites

Complex analysis 1

Study materials

Kilpeläinen: Kompleksianalyysi (luentomonisteet www-sivulla).

Literature

  • B.P. Palka: An Introduction to Complex Function Theory; ISBN: 0-387-97427-X
  • Eberhard Freitag ja Rolf Busam: Complex analysis, toinen laitos, Universitext, Springer, 2009.

Completion methods

Method 1

Evaluation criteria:
Course exam and exercises
Time of teaching:
Period 4
Select all marked parts

Method 2

Evaluation criteria:
Final exam
Select all marked parts
Parts of the completion methods
x

Teaching (5 cr)

Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
Kurssitenttiin saa lisäpisteitä tehdyistä harjoitustehtävistä opetusohjelmassa ilmoitettavan laskutavan mukaisesti. Opintojakson arvosana määräytyy kurssitentin pistemäärän ja laskuharjoitushyvitysten summan perusteella. Hyväksyttyyn suoritukseen vaaditaan vähintään puolet maksimipistemäärästä.
Language:
English, Finnish

Teaching

x

Exam (5 cr)

Type:
Exam
Grading scale:
0-5
Evaluation criteria:
Hyväksyttyyn suoritukseen vaaditaan vähintään puolet lopputentin maksimipistemäärästä.
Language:
English, Finnish

Teaching