Concepts of Function Theory - Real and Complex Analysis of one Variable
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| Verlag | Springer |
| Auflage | 2025 |
| Seiten | 274 |
| Format | 15,5 x 1,5 x 23,5 cm |
| Gewicht | 538 g |
| Artikeltyp | Englisches Buch |
| Reihe | Mathematics Study Resources 12 |
| ISBN-10 | 3662691140 |
| EAN | 9783662691144 |
| Bestell-Nr | 66269114A |
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.
Inhaltsverzeichnis:
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.
