Functions of a Complex Variable

Course code

MLM6312.DT

old course code

MLM6312

Course title in Estonian

Kompleksmuutuja funktsioonid

Course title in English

Functions of a Complex Variable

ECTS credits

6.0

approximate amount of contact lessons

56

Teaching semester

autumn

Assessment form

Examination

lecturer of 2019/2020 Spring semester

õppejõud on määramata

lecturer of 2020/2021 Autumn semester

lecturer not assigned

Course aims

To generalize basic notions and results known for functions of real variables for functions of a complex variable. To develop basic skills for solving problems, and to demonstrate different types of applications. Special attention is paid? to relations between the present course and previous courses in mathematical analysis.

Brief description of the course

Concept of function of complex variable, limit and continuity, analytical functions. Conformal mapping. Integral of complex variable functions. Cauchy Theorem. Cauchy Formula. Taylor and Laurent series. Singularity points and residues. Applications of residues.

Independent work

Homeworks on lecture materials, literature and problem solving. Preparations for classroom tests and final examination.

Learning outcomes in the course

Student knows mathematical facts and is able to use methods in volume of the subject.

Assessment methods

The examination grade is based on the total number of points gained from written tests completed during the semester and a final examination. The maximal number of points (100) is equally divided between current semester work and final examination.

Teacher

prof Anne Tali

Prerequisite course 1

Study literature

Jürimäe, E. 1983 Kompleksmuutuja funktsioonide teooria lühikursus. Tallinn: Valgus;

Conway, J. B. 1984 Functions of one complex variable. New York, Berlin, Heidelberg: Springer-Verlag;

Saff, E. B.; Snider, A. D. 2003 Fundamentals of Complex Analysis. Prentice Hall.

Conway, J. B. 1984 Functions of one complex variable. New York, Berlin, Heidelberg: Springer-Verlag;

Saff, E. B.; Snider, A. D. 2003 Fundamentals of Complex Analysis. Prentice Hall.