E-Book, Englisch, Band 12, 274 Seiten, eBook
Reihe: Mathematics Study Resources
Müller Concepts of Function Theory
Erscheinungsjahr 2025
ISBN: 978-3-662-69115-1
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
Real and Complex Analysis of one Variable
E-Book, Englisch, Band 12, 274 Seiten, eBook
Reihe: Mathematics Study Resources
ISBN: 978-3-662-69115-1
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Zielgruppe
Upper undergraduate
Autoren/Hrsg.
Weitere Infos & Material
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.