MS-C1300: Complex Analysis
| Course name | Complex Analysis |
|---|---|
| Course code | MS-C1300 |
| Abbreviation | “Kompleksi” |
| Period | II |
| Lecturer | Kalle Kytölä |
Description
The course could be described as Calculus 4, as it partly continues discussing similar topics expanding them on the complex plane. The course is well-organized and nice to follow. Upon successful completion of this course, you should be able to make use of complex numbers in solving geometric problems, be able to solve mapping problems in the plane, recognize the behavior of complex functions, be able to interpret basic properties of analytic (holomorphic and meromorphic) functions and be able to calculate real integrals by making use of complex integrals.
Course material
Official material
There are lecture notes from previous years as well as a GitHub document that updates during the course. Some of the notes can be trickier to read due to handwriting, but there should not be any lack of available materials. Zulip is utilised as a Q&A channel.
Extra material
YouTube playlist: Engineering Math: Crash Course in Complex Analysis, Steve Brunton https://youtube.com/playlist?list=PLMrJAkhIeNNQBRslPb7I0yTnES981R8Cg&si=wbWqVeBg_BFa-7Pp
Contents and workload
The course requires a steady amount of work throughout the period due to two different homework sheets per week.
Overall workload
Weekly contents
| Week | Topics |
|---|---|
| 1 | The Complex Number System |
| 2 | Complex Derivatives and Analytic Functions |
| 3 | Contour Integration |
| 4 | Cauchy’s Theorem and Consequences |
| 5 | Power Series |
| 6 | Isolated Singularities and Residues |
Practicalities
There are two completion methods:
- The homework exercises contribute to the final grade.
- Final exam only.
Related courses
Official prerequisites
MS-A02XX
Additional prerequisites
In addition, Metric Spaces may offer further intuition to the topics. However, it is possible to successfully complete the course also without it.
More like this
Trivia
Timestamp
Based on the 2026 version.