Concepts of Function Theory Real and Complex Analysis of One Variable |
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| Author:
| Müller, Jürgen |
| Series title: | Mathematics Study Resources Ser. |
| ISBN: | 978-3-662-69114-4 |
| Publication Date: | Jul 2024 |
| Publisher: | Springer Berlin / Heidelberg
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| Imprint: | Springer |
| Book Format: | Paperback |
| List Price: | USD $54.99 |
Book Description:
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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...
More Description
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.