COURSE SYLLABUS

Complex analysis 7.5 credits

Komplex analys
First cycle, M0054M
Version
Course syllabus valid: Autumn 2021 Sp 1 - Present
The version indicates the term and period for which this course syllabus is valid. The most recent version of the course syllabus is shown first.

 Education level First cycle Grade scale G U 3 4 5 Subject Mathematics Subject group (SCB) Mathematics

Entry requirements

In order to meet the general entry requirements for first cycle studies you must have successfully completed upper secondary education and documented skills in English language and the courses Differential Calculus M0047M), Linear Algebra and Calculus (M0048M), Linear Algebra and Differential Equations (M0049M)and the course Multivariable Calculus (M0055M) or their equivalent.

Selection

The selection is based on 1-165 credits.

Course Aim
After completed course, the students should be able to:
• give an account of the definitions and properties for the elementary functions.
• give an account of the basic theory of analytic functions, with the important theorems like Cauchy’s integral theorem, Cauchy’s integral formula, Liouville’s theorem, the identity principle etc.
• give an account of the maximum principle for analytic and for harmonic functions.
• solve Dirichlet’s problem in simple domains using analytic functions and conformal mappings.
• give an account for the theory of power series and its connection with analytic functions.
• determine Taylor and Laurent series and give an account of the convergence.
• calculating integrals using the Residue theorem.
• give an account of the theory of conformal mapping. In particular Möbius mappings including cross-ratio and the symmetry principle.
• give an account of the argument principle and using it to determine the number of zeros in domain like the first quadrant.

Contents
This course treats basic theory of analytic functions such as Cauchy-Riemann’s equation, the elementary functions, integration in the complex plane, Cauchy’s integral theorem, Cauchy’s integral formula and its consequences, Taylor series, power series and Laurent series, the residue theorem, the argument principle, Rouché’s theorem and conformal mappings.

Realization
Each course occasion´s language and form is stated and appear on the course page on Luleå University of Technology's website.
The teaching consists of lectures and tutorials. The main learning is achieved by home studies, mainly problem solving.

Examination
If there is a decision on special educational support, in accordance with the Guideline Student's rights and obligations at Luleå University of Technology, an adapted or alternative form of examination can be provided.
The course aims are examined by a written individual exam. Grading according to the scale G U 3 4 5.

Transition terms
The course replaces M0012M

Examiner
Stefan Ericsson

Literature. Valid from Autumn 2019 Sp 1
Fundamentals of Complex Analysis, E.B. Saff & A.D. Snider, Latest edition, Pearson

Course offered by
Department of Engineering Sciences and Mathematics

Modules