FYSS7301 Complex Analysis (5 cr)
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.
Study methods
Assignments, examination
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鈥檚 theorem and Cauchy鈥檚 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
Further information
Spring semester 1st period, every two years starting spring 2019.
Materials
Lecture notes by Kari J. Eskola
Literature:
| ISBN-number | Author, year of publication, title, publisher |
|---|---|
| 0-13-321431- | Michael D. Greenberg: Advanced Engineering Mathematics (Prentice Hall), ISBN 0-13-321431-1 |
| 07-060230-1 | Murray R. Spiegel: Theory and problems of complex variables, Schaum's outline series (McGraw-Hill), ISBN 07-060230-1 |
| 951-745-211-X | Juha Honkonen: Fysiikan matemaattiset menetelm盲t I (Limes, 2005), ISBN 951-745-211-X |
| 0-12-059810-8 | George Arfken: Mathematical Methods for Physicists (Academic Press), ISBN 0-12-059810-8 |
Assessment criteria
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.
Prerequisites
MATP211-213, MATA181-182