FYSS7301 Complex Analysis (5 cr)
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
Method 2
Teaching (5 cr)
Lectures, exercises and exam.
Teaching
1/10–3/18/2023 Lectures
4/14–4/14/2023 Exam
Independent study (5 cr)
Independent studying, exercises and exam.