MATS122 Complex Analysis 2 (5 cr)
Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2024-2025, 2025-2026, 2026-2027, 2027-2028
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 (luentomoniste).
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
Language:
English, Finnish
Teaching
3/20–5/25/2025 Lectures
5/21–5/21/2025 Course Exam
x
Exam (5 cr)
Type:
Exam
Grading scale:
0-5
Language:
English, Finnish