SF1691 Complex Analysis 7.5 credits

Komplex analys

  • Education cycle

    First cycle
  • Main field of study

    Technology
  • Grading scale

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

Course offerings

Intended learning outcomes

After the course the student should be able to

  • Manipulate, interpret and use the basic concepts: complex number, analytic function, harmonic function, Taylor and Laurent series, singularity, residue, conformal mapping, meromorphic function.
  • Relate different possible definitions of the term analytic function to each other and determine if a given function is analytic.
  • Derive certain basic properties of analytic function, e.g. Cauchy's formula.
  • Explain how analytic functions are used in connection to signals and systems. The focus is on the Laplace and Z-transform.
  • Use conformal mapping to solve certain applied problems regarding heat conduction, electrical engineering and fluid mechanics. Especially, also use the Poisson kernel to solve boudary value problems for the Laplace equation.
  • 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 receive a higher grade 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

SF1672 Linear Algebra, SF1673 Calculus in One Variable and SF1674 Multivariable Calculus, or corresponding courses.

Literature

The course literature is announced on the course webpage four week before the start of the course.

Examination

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

Offered by

SCI/Mathematics

Examiner

Håkan Hedenmalm <haakanh@kth.se>

Version

Course syllabus valid from: Spring 2019.
Examination information valid from: Spring 2019.