401-2303-00L  Complex Analysis

SemesterAutumn Semester 2021
LecturersT. H. Willwacher
Periodicityyearly recurring course
Language of instructionGerman

AbstractComplex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, index of closed curves, analytic continuation, special functions, conformal mappings, Riemann mapping theorem.
ObjectiveWorking knowledge of functions of one complex variables; in particular applications of the residue theorem.
LiteratureB. Palka: "An introduction to complex function theory."
Undergraduate Texts in Mathematics. Springer-Verlag, 1991.

E.M. Stein, R. Shakarchi: Complex Analysis. Princeton University Press, 2010

Th. Gamelin: Complex Analysis. Springer 2001

E. Titchmarsh: The Theory of Functions. Oxford University Press

D. Salamon: "Funktionentheorie". Birkhauser, 2011. (In German)

L. Ahlfors: "Complex analysis. An introduction to the theory of analytic functions of one complex variable." International Series in Pure and Applied Mathematics. McGraw-Hill Book Co.

K.Jaenich: Funktionentheorie. Springer Verlag

R.Remmert: Funktionentheorie I. Springer Verlag

E.Hille: Analytic Function Theory. AMS Chelsea Publications