SF1628 Complex Analysis 6.0 credits

Komplex analys

Please note

This course has been cancelled.

Basic course of analytic functions.

  • Education cycle

    First cycle
  • Main field of study

    Mathematics
    Technology
  • Grading scale

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

Last planned examination: spring 20.

At present this course is not scheduled to be offered.

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 main content

  • 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.

Eligibility

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

  • TEN1 - Examination, 6.0, grading scale: A, B, C, D, E, FX, F

Requirements for final grade

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

Offered by

SCI/Mathematics

Examiner

Håkan Hedenmalm <haakanh@kth.se>

Version

Course syllabus valid from: Autumn 2013.
Examination information valid from: Autumn 2007.