Skip to main content
Till KTH:s startsida

SF1628 Complex Analysis 6.0 credits

Administer About course

Information per course offering

Course offerings are missing for current or upcoming semesters.

Course syllabus as PDF

Please note: all information from the Course syllabus is available on this page in an accessible format.

Course syllabus SF1628 (Autumn 2013–)
Headings with content from the Course syllabus SF1628 (Autumn 2013–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

  • Meromorphic and analytic functions of one complex variable. Basic transcendental functions, harmonic functions.
  • Integration in the complex plane, Cauchy’s theorem, Cauchy’s integral formula and consequences thereof. Residues.
  • Taylor and Laurent series, zeros and poles, the principle of the argument.
  • Conformal mapping and applications.

Intended learning outcomes

After the course the student should be able to

  • Understand, interpret and use the basic concepts: complex number, analytic function, harmonic function, Taylor and Laurent series, singularity, residue, conformal mapping, meromorphic function.
  • Prove certain fundamental theorems about analytic functions, e.g. Cauchy’s integral formula
  • Determine the stability of certain dynamical systems using the Nyqvist criterion
  • Use conformal mapping to solve certain applied problems regarding heat conduction, electrical engineering and fluid mechanics.
  • Use Taylor and Laurent expansions to derive properties of analytic and meromorphic functions.
  • Compute integrals by means of residues.
  • Analyze zeros and poles of meromorphic functions, classify singularities.

In order to get a higher the student should also be able to

  • Explain the theory of analytic functions and prove the most important theorems.

Literature and preparations

Specific prerequisites

Calculus, introductory courses, SF1602 + SF1603 and SF1604 Linear Algebra.

Literature

Saff&Snider: 
Fundamentals of Complex Variables with Applications to Engineerin and Science, 3:rd ed. 

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

Examination

  • TEN1 - Examination, 6.0 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.

Other requirements for final grade

Written and/or oral examination, possibly in conjunction with certain other assignments.

Examiner

Profile picture Lars Filipsson

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

SCI/Mathematics

Main field of study

Mathematics, Technology

Education cycle

First cycle