FYSS7301 Kompleksianalyysi (5 op)

Osaamistavoitteet

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.

Suoritustavat

Assignments, examination

Sisältö

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

Lisätiedot

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

Oppimateriaalit

Lecture notes by Kari J. Eskola

Kirjallisuus

Arviointiperusteet

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.

Esitietovaatimukset

MATP211-213, MATA181-182

Vastaavat opintojaksot

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