SoSe 22: Theory of Functions
Alexander Schmitt
Comments
Function theory is a classical field of mathematics, which deals with the properties of complex-differentiable functions on the complex number plane and has connections to algebra, analysis, number theory and geometry.
The concept of complex differentiability restricts real-differentiable functions from R2 to R2 to angle-preserving images. We will discover that complex-differentiable functions are quite rigid objects, but they are endowed with many amazing analytical, geometric, and visual properties.
A major result discussed in this lecture is Cauchy's integral theorem which states that the integral of any complexly differentiable function along a closed path in the complex plane is zero. We will see many nice consequences of this result, e.g. Cauchy's integral formula, the residual theorem and a proof of the fundamental theorem of algebra, as well as modern graphical representation methods.
closeSuggested reading
Wolfgang Fischer, Ingo Lieb: Funktionentheorie. 8. Auflage. Vieweg, Braunschweig 2003, ISBN 3-528-77247-6.
T. Needham: Anschauliche Funktionentheorie, Oldenbourg Wissenschaftsverlag, (2001).
Reinhold Remmert, Georg Schumacher: Funktionentheorie 1. 5. Auflage. Springer, Berlin 2002, ISBN 3-540-59075-7
26 Class schedule
Additional appointments
Mon, 2022-07-25 12:00 - 14:00Regular appointments