Course unit, curriculum year 2023–2024
MATH.APP.440
Complex functions, 5 cr
Tampere University
- Description
- Completion options
Teaching periods
Active in period 1 (1.8.2023–22.10.2023)
Active in period 4 (4.3.2024–31.5.2024)
Active in period 5 (1.6.2024–31.7.2024)
Course code
MATH.APP.440Language of instruction
English, FinnishAcademic years
2021–2022, 2022–2023, 2023–2024Level of study
Intermediate studiesGrading scale
General scale, 0-5Persons responsible
Responsible teacher:
Petteri Laakkonen, Responsible for course implementationsResponsible teacher:
Lassi PaunonenResponsible organisation
Faculty of Information Technology and Communication Sciences 100 %
Coordinating organisation
Computing Sciences Studies 100 %
Core content
- Complex numbers, basic operations and their geometric interpretation.
- Elementary complex functions and their properties.
- Continuity, differentiability and analyticity of complex functions. Cauchy-Riemann equations.
- Complex Integral and the related basic results: The fundamental theorem of analysis, Cauchy-Goursat theorem, Cauchy's integral theorem, Cauchy's integral formulas, and deformation theorem.
- Taylor's and Laurent's series and their applications: Singularities and Residue calculus.
Complementary knowledge
- Visualization of complex functions
- Applying residues to calculate real integrals.
Specialist knowledge
- Liouville’s theorem and the fundamental theorem of algebra as a consequence of Cauchy’s integral formula
- Applications: Harmonic functions and/or conformal mappings
Learning outcomes
Prerequisites
Compulsory prerequisites
Recommended prerequisites
Learning material
Equivalences
Studies that include this course
Completion option 1
This is the preferred method for competing the course which you may attend also online. The course grade is determined by the activity during the course (weight 2/3) and final exam (weight 1/3) both related to the same course implementation.
Completion of all options is required.
Participation in teaching
05.03.2024 – 31.05.2024
Active in period 4 (4.3.2024–31.5.2024)
Completion option 2
If you cannot attend the course activities actively, you may complete the course by passing the exam.