Mathematics Study Resources: Real and Complex Analysis of one Variable

Müller, Jürgen

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.

Details

Published by: Springer

Publication Date: 2025-03-02

Format: Paperback

ISBN-13: 9783662691144

DOI: 10.1007/978-3-662-69115-1

Dimensions: 235cm x155cm

Pages: 274