Course syllabus

Matematik - Funktionsteori
Mathematics - Analytic Functions

FMAF01, 7 credits, G2 (First Cycle)

Valid for: 2015/16
Decided by: Education Board B
Date of Decision: 2015-04-16

General Information

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


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, recursive 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
Assessment: Written test comprising theory and problems. Computer work and written assignments which should be completed BEFORE the exam.

Code: 0108. Name: Analytic Functions.
Credits: 7. Grading scale: TH.
Code: 0208. Name: Computer Laboratory Work.
Credits: 0. Grading scale: UG.


Admission requirements:

Required prior knowledge: Linear algebra (FMA420) and calculus in one and several variables (FMAA01/FMAA05 and FMA430).
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 homepage:
Further information: The written exams on the course also count as exams on the earlier courses FMA280 and FMA037. In order for an exam to be graded it is necessary that the examinee has passed on the assignments and the computer sessions before the exam.