Course syllabus

Matematik - Funktionsteori
Mathematics - Analytic Functions

FMAF01, 7 credits, G2 (First Cycle)

Valid for: 2018/19
Decided by: PLED F/Pi
Date of Decision: 2018-03-23

General Information

Main field: Technology.
Compulsory for: E2, F2, I2, Pi2
Elective Compulsory for: D2
Elective for: BME4, C4, M4, N3
Language of instruction: The course will be given in English on demand


The aim is to provide concepts and methods from real and complex analysis which are important for further studies within for example mathematics, economy, physics, field theory, mathematical statistics, control theory, signal theory, and for professional work in the future. The aim is also to make the students develop their ability to solve problems, to assimilate mathematical text and to communicate mathematics.

Learning outcomes

Knowledge and understanding
For a passing grade the student must

Competences and skills
For a passing grade the student must


Sums and series: sequences, difference equations, numerical series, absolute and conditional convergence. Function sequences and function series. Norms of functions and uniform convergence.

Power series: radius of convergence, integration and differentiation of power series, power series expansions of the elementary functions.

Fourier series: exponential and trigonometric Fourier series, questions of convergence, Parseval's formula.

Analytic functions: definition of an analytic function, the Cauchy-Riemann equations. Elementary analytic functions. Cauchy's integral theorem and integral formula. Expansion in power series. The identity theorem. The residue theorem. Calculation of real integrals by residue calculus.

Examination details

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)
Assessment: Written test comprising theory and problems. Assignments, requiring work with and without computer, which have to be completed BEFORE the exam.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Code: 0116. Name: Analytic Functions.
Credits: 7. Grading scale: TH.
Code: 0216. Name: Assignments.
Credits: 0. Grading scale: UG.


Admission requirements:

Required prior knowledge: Linear algebra (FMAB20) and calculus in one and several variables (FMAA01/FMAA05 and FMAB30).
The number of participants is limited to: No
The course overlaps following course/s: FMA030, FMA037, FMA280

Reading list

Contact and other information

Course coordinator: Studierektor Anders Holst,
Course administrator: Studerandeexpeditionen,
Course homepage:
Further information: In order for an exam to be graded it is necessary that the examinee has passed on the assignments before the exam.