FYSS7301 Complex Analysis (6 cr)

Open the course unit brochure on Sisu
Study level:
Advanced studies
Grading scale:
0-5
Language:
English
Responsible organisation:
Department of Physics
Curriculum periods:
2024-2025, 2025-2026, 2026-2027, 2027-2028

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 

  • Gamma function in the complex plane

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 (or the lecturer)

Literature

  • 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
  • Juha Honkonen: Fysiikan matemaattiset menetelmät I (Limes, 2005), ISBN 951-745-211-X

Completion methods

Method 1

Description:
This completion method is recommended: lectures+exercises+final exam. The course is given every two years, starting spring 2025.
Evaluation criteria:
Exercises (max 12 p) and exam (max 48 p) = max 60 p
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. living elsewhere). Contact the teacher before enrolling to the course via this completion method.
Evaluation criteria:
Exercises (max 12 p) and exam (max 48 p) = max 60 p.
Select all marked parts
Parts of the completion methods
x

Participation in teaching (6 cr)

Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
<p>Exercises and final exam. Weights: exercises 1/5 and final exam 4/5.</p>
Language:
English
Study methods:

Lectures and exercises + final exam.

Study materials:

Lecture notes by Kari J. Eskola or by the lecturer

Teaching

x

Independent study (6 cr)

Type:
Independent study
Grading scale:
0-5
Evaluation criteria:
<p>Exercises and exam.&nbsp;Weights: exercises 1/5 and final exam 4/5.</p>
Language:
English
Study methods:

Independent studying, exercises and final exam. 

Study materials:

Lecture notes by Kari J. Eskola or the lecturer

Teaching