MAT2410 – Introduction to Complex Analysis

Schedule, syllabus and examination date

Choose semester

Course content

MAT2410 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 will be able to:

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

Admission

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.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.

Prerequisites

Formal prerequisite knowledge

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).

Recommended previous knowledge

MAT1100 – Calculus and MAT1110 – Calculus and Linear Algebra. It will be useful to have taken MAT2400 – Real Analysis, but this is not a prerequisite for the course.

Overlapping courses

10 credits overlap with MAT2300 – Analysis II (discontinued)

*The information about overlaps for discontinued courses may not be complete. If you have questions, please contact the Department. 

Teaching

6 hours of lectures/exercises per week.

Examination

2 mandatory assignments.

Final written examination.

Examination support material

No examination support material is allowed.

Language of examination

Subjects taught in English will only offer the exam paper in English.

You may write your examination paper 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.

Explanations and appeals

Resit an examination

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

Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

Evaluation

The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

Facts about this course

Credits

10

Level

Bachelor

Teaching

Every autumn

Examination

Every autumn

Teaching language

English

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