# 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.