Sinopsis
An accessible, rigorous introduction to complex functions that unites core methods
This edition presents the theory of functions of a complex variable with clear aims: to introduce beginning students to both the geometric and analytic viewpoints. It blends Riemann’s geometric approach with Weierstrassian rigor, showing how each method contributes to understanding complex functions.
Topics move from the basics of complex numbers and their geometric representation to single-valued analytic functions, the exponential and trigonometric functions, and the ideas behind conformal representations. The text also surveys the RIEMANN surface, the notion of analytic continuation, and related theorems that structure the subject.
- Foundations: complex numbers, geometry, and basic representations
- Analytic theory: regular functions, derivatives, and integrals
- Special functions: exponential, sine, cosine, and their identities
- Conformal mappings and geometric transformations
- Introductory concepts of the RIEMANN surface and analytic continuation
Ideal for readers beginning a study of complex analysis or seeking a solid, practical overview of the subject.
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Reseña del editor
Excerpt from Theory of Functions of a Complex Variable
In the first chapter, I have introduced the algebra of complex num bers as an algebra of number-pairs without giving a general theory of number systems of two (or more) units; I have rather assumed with out discussion the hypotheses characteristic of the theory of ordinary complex numbers.
The second chapter contains a detailed geometrical theory of the elementary rational functions of a complex variable and the conformal representations determined by them. The transition from the plane to the sphere by stereographic projection is also considered; it is used at various places in the following chapters. The chapter closes with a discussion of the symmetric invariants of four points as a function of their double ratio; this takes the place of an example (in itself unimportant) of a rational function of a more general character.
About the Publisher
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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Reseña del editor
Theory ofF unctions of aC omplex Variable written in English and adapted in other ways to the use of students beginning their graduate work. Professor Burkhardt sbook Einfnhrung in dieT heorie der analytischen Funktionen einer komplexen Ver dnderlicheti has seemed admirably suited to this purpose both in the matter of material and arrangement. The translation of this text into English was undertaken at the suggestion and encouragement of prominent American mathematicians, sinct there is no book in theE nglish language treating the subject from the point of view adopted here. The translation preserves the same arrangement of material as the original book, even to the numbering of sections and theorems. Footnotes not in the original text are always signed. All of the exercises, which include a number of additional fig ures and which follow various sections and each of the chap ters, are added by the translator. It is hoped that they will prove of assistance not only in illustrating and fixing the ideas contained in the text but as well in stimulating the reader to independent attack and further study in larger treatises.
(Typographical errors above are due to OCR software and don't occur in the book.)
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Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology.
Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the aged text. Read books online for free at www.forgottenbooks.org
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Theory of Functions of a Complex Variable (Classic Reprint)
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Paperback. Condición: New. Print on Demand. This seminal book from the 19th century introduces beginners to the theory of functions, a foundational concept in modern mathematics. Derived from trigonometry, it profoundly impacted geometry and the study of complex numbers. The author provides a detailed look at rational functions and conformal representations determined by them. He adeptly guides the reader through proofs of fundamental theorems and discusses transformations of the plane into itself. The ideas and techniques laid out in this book helped pave the way for further exploration in the field of complex analysis. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Nº de ref. del artículo: 9781440040368_0
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Theory of Functions of a Complex Variable (Classic Reprint)
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Theory of Functions of a Complex Variable: Authorized Translation from the Fourth German Edition (Classic Reprint)
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Paperback. Condición: Brand New. 434 pages. 9.00x6.00x0.98 inches. This item is printed on demand. Nº de ref. del artículo: zk1440040362
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