Concepts of Function Theory

Prof. Dr. Jürgen Müller is a lecturer in the Department of Mathematics at the University of Trier. He conducts research in the field of complex analysis of one variable, focusing particularly on approximation in the complex domain. His motivation for writing this textbook stemmed from the idea of demonstrating a direct approach to function theory from the fundamentals of analysis, thereby enabling an immediate entry into the theory.

• Rules of the Game: Sets, mappings, numbers.- Basics: Limits, elementary functions, and metric spaces.- Up and Down: Differentiation and integration; Magic Circles: Circular functions and local function theory.- Wonder Worlds: Global function theory.- Normal or Not: Conformal mappings and complex dynamics.- Extras: Runge theory and applications.