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SF2745 Advanced Complex Analysis 7.5 credits

About course offering

For course offering

Spring 2024 Start 16 Jan 2024 programme students

Target group

Elective for all programmes as long as it can be included in your programme.

Part of programme

Master's Programme, Mathematics, åk 1, Optional

Master's Programme, Mathematics, åk 2, Optional


P3 (3.7 hp), P4 (3.8 hp)


16 Jan 2024
3 Jun 2024

Pace of study


Form of study

Normal Daytime

Language of instruction


Course location

KTH Campus

Number of places

Places are not limited

Planned modular schedule


For course offering

Spring 2024 Start 16 Jan 2024 programme students

Application code



For course offering

Spring 2024 Start 16 Jan 2024 programme students


Fredrik Viklund (


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Course coordinator

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Headings with content from the Course syllabus SF2745 (Spring 2020–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Generalizations of Cauchy’s integral formula, analytic continuation, normal families and the Riemann mapping theorem, special classes of conformal maps, complex differential equations.

Suggested applications:

  • Hardy spaces
  • Boundary behavior of analytic functions
  • Riemann-Hilbert problems
  • Harmonic functions and harmonic measure
  • Infinite products of analytic functions

Intended learning outcomes

After the course the student should be able to:

  • formulate and prove theorems concerning analytic functions such as, e.g., the generalized Cauchy integral formula and the Riemann mapping theorem;
  • use and analyze conformal maps;
  • discuss the theory of analytic continuation and properties of solutions to complex differential equations;
  • be able to use this knowledge in the context of further applications

Literature and preparations

Specific prerequisites

Completed courses SF1677 Foundations of mathematical analysis and SF1691 Complex analysis.

Recommended prerequisites

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Announced no later than 4 weeks before the start of the course on the course web page.

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

A, B, C, D, E, FX, F


  • TEN1 - Exam, 7.5 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

The examiner decides about adapted examination for students with documented, severe disabilities in consultation with the contact person for disabilities at KTH (Funka). The examiner may allow a different form of examination for re-examination of individual students.

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

Main field of study


Education cycle

Second cycle

Add-on studies

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Fredrik Viklund (