SF1628 Complex Analysis 6.0 credits
This course has been cancelled.
Basic course of analytic functions.
Education cycleFirst cycle
Main field of studyMathematics
Grading scaleA, 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.
Calculus, introductory courses, SF1602 + SF1603 and SF1604 Linear Algebra.
Fundamentals of Complex Variables with Applications to Engineerin and Science, 3:rd ed.
- 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.
Håkan Hedenmalm <email@example.com>
Course syllabus valid from: Autumn 2013.
Examination information valid from: Autumn 2007.