SF1628 Complex Analysis 6.0 credits

Komplex analys

Basic course of analytic functions.

Offering and execution

Course offering missing for current semester as well as for previous and coming semesters

Course information

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.

Course Disposition

No information inserted

Literature and preparations

Specific prerequisites *

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

Recommended prerequisites

No information inserted

Equipment

No information inserted

Literature

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

Examination and completion

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.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

Lars Filipsson

Further information

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SF1628

Offered by

SCI/Mathematics

Main field of study *

Mathematics, Technology

Education cycle *

First cycle

Add-on studies

No information inserted

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.