FYSS7301 Complex Analysis (5 cr)

Open the course unit brochure on Sisu
Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Physics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023

Description

  • Complex numbers and elementary functions of complex variables

  • Derivative and analyticity of a function of complex variables

  • Contour integration in the complex plane

  • Cauchy’s theorem and Cauchy’s integral formulae

  • Taylor series and analytic continuation

  • Laurent series, classification of singularities and calculation of residues

  • Residue theorem, with various applications in contour integrals in the complex plane, summation of series and infinite products 

Learning outcomes

After this course, the student will

  • knows how to deal with functions of complex variables

  • understands the concept of analyticity of a function and can apply this especially in contour integrals in the complex plane

  • knows the concept of analytical continuation

  • be able to form Laurent series of functions of complex variables, understands the classification of singularities and is able to apply these in finding the residues

  • knows what is the residue theorem and is able to apply this in contour integrals in the complex plane and also in summation of series 

Description of prerequisites

  • MATP211 Calculus 1

  • MATA181-MATA182 Vektoricalculus 1 and 2 or similar.  

Study materials

Lecture notes by Kari J. Eskola

Literature

  • Juha Honkonen: Fysiikan matemaattiset menetelmät I (Limes, 2005), ISBN 951-745-211-X
  • Murray R. Spiegel: Theory and problems of complex variables, Schaum's outline series (McGraw-Hill), ISBN 07-060230-1
  • Michael D. Greenberg: Advanced Engineering Mathematics (Prentice Hall), ISBN 0-13-321431-1
  • George Arfken: Mathematical Methods for Physicists (Academic Press), ISBN 0-12-059810-8

Completion methods

Method 1

Description:
Given every two years starting spring 2021.
Evaluation criteria:
Exercises and exam.
Time of teaching:
Period 3
Select all marked parts

Method 2

Description:
This completion method is intended for students for whom method 1 is not possible for specific reasons (e.g. language, living elsewhere). Contact the teacher before enrolling to the course via this completion method.
Evaluation criteria:
Exercises and exam.
Select all marked parts
Parts of the completion methods
x

Teaching (5 cr)

Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
Exercises and exam.
Language:
English
Study methods:

Lectures, exercises and exam. 

No published teaching
x

Independent study (5 cr)

Type:
Independent study
Grading scale:
0-5
Evaluation criteria:
Exercises and exam.
Language:
English, Finnish
Study methods:

Independent studying, exercises and exam. 

Teaching