FYSS7301 Complex Analysis (5 cr)

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Study level:
Advanced studies
Grading scale:
0-5
Language:
English
Responsible organisation:
Department of Physics
Curriculum periods:
2017-2018, 2018-2019, 2019-2020

Description

Content

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

Completion methods

Assignments, examination

Assessment details

Maximum points: 80% from the final exam plus 20% from the exercises; passing the course: at least 50% of the maximum total points obtained; maximum score from the exercises: at least 80% of all the available exercise points obtained.

Learning outcomes

At the end of this course, students will be able to deal with functions of complex variables. Students will be able to study the analyticity of a function and make use of the analyticity especially in contour integrals in the complex plane, perform analytic continuation and form Laurent series of functions of complex variables. They will also be able to classify the singularities and find the residues of a function, apply the residue theorem to perform various types of contour integrals in the complex plane and do summation of series with the residue theorem.

Additional information

Spring semester 1st period, every two years starting spring 2019.

Description of prerequisites

MATP211-213, MATA181-182

Study materials

Lecture notes by Kari J. Eskola

Literature

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

Completion methods

Method 1

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Parts of the completion methods
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Teaching (5 cr)

Type:
Participation in teaching
Grading scale:
0-5
Language:
English

Teaching