MAT2410 – Introduction to Complex Analysis

Schedule, syllabus and examination date

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Exams after the reopening

As a general rule, exams will be conducted without physical attendance in the autumn of 2021, even after the reopening. See the semester page for information about the form of examination in your course. See also more information about examination at the MN Faculty in 2021.

Course content

This course gives an introduction to the theory of functions of one complex variable. Central themes in the course are analytic and harmonic functions and their properties, power series and Laurent series, isolated singularities, Cauchy´s integral theorem and residue calculus, the maximum principle, Schwarz lemma, and conformal mappings.

Learning outcome

After completing the course you

  • can carry out computations with the complex exponential, logarithm and root functions and know their domains of definition
  • are able to calculate the image of circles and lines under Möbius transformations
  • can find the harmonic conjugate to a harmonic function
  • can express analytic functions in terms of power series and Laurent series
  • are able to calculate complex line integrals and some infinite real integrals using Cauchy´s integral theorem or residue calculus
  • can find the number of zeroes and poles within a given curve using the argument principle or Rouche´s theorem
  • can calculate the flow lines of an irrotational and incompressible fluid.

Admission to the course

Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

Special admission requirements

In addition to fulfilling the Higher Education Entrance Qualification, applicants have to meet the following special admission requirements:

  • Mathematics R1 (or Mathematics S1 and S2) + R2

And in addition one of these:

  • Physics (1+2)

  • Chemistry (1+2)

  • Biology (1+2)

  • Information technology (1+2)

  • Geosciences (1+2)

  • Technology and theories of research (1+2)

The special admission requirements may also be covered by equivalent studies from Norwegian upper secondary school or by other equivalent studies (in Norwegian).

Overlapping courses


6 hours of lectures/exercises per week throughout the semester.

The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.


Final written exam which counts 100 % towards the final grade. 

This course has 2 mandatory assignments that must be approved before you can sit the final exam.

Examination support material

No examination support material is allowed.

Language of examination

Courses taught in English will only offer the exam paper in English. You may submit your response in Norwegian, Swedish, Danish or English.

Grading scale

Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

Resit an examination

This course offers both postponed and resit of examination. Read more:

Special examination arrangements, use of sources, explanations and appeals

See more about examinations at UiO

Last updated from FS (Common Student System) Oct. 26, 2021 8:33:42 PM

Facts about this course

Teaching language