Concepts of Function Theory : Real and Complex Analysis of one Variable

This textbook presents a direct path from real analysis of one variable to function theory.

Classical topics of one-dimensional real analysis, such as differential and integral calculus, are largely presented from a complex perspective.

The goal is a self-contained exposition extending to the Runge theorems and the dynamics of entire functions.

Short sections appended to each chapter on concepts of function theory provide glimpses into higher-dimensional analysis and an impression of its universal significance for mathematics.

The book is structured so that parts can also serve as a basis for a seminar.  Thus, this fascinating area of mathematics becomes accessible to students whose programs do not focus on mathematics and for whom a classical introduction to function theory would be too time-consuming.

This book enables them to take a step into complex analysis, through which they can recognize a multitude of connections that remain hidden in real analysis.  The translation was done with the help of artificial intelligence.

A subsequent human revision was done primarily in terms of content.