Theory of Functions of a Complex Variable (Classic Reprint) - Couverture souple

Burkhardt, Heinrich

Couverture souple

ISBN 10 : 1440040362 ISBN 13 : 9781440040368

Editeur : Forgotten Books, 2018

Synopsis

Explore the theory of functions of a complex variable, presented as an accessible, unified introduction

This edition surveys the central ideas in complex analysis, weaving together geometric intuition and rigorous proofs. It blends classical approaches and modern developments to help beginners grasp how complex numbers behave under analytic methods, with careful attention to foundational concepts and key theorems.

The book opens by building the algebra and geometry of complex numbers, then moves through rational and again to many-valued functions. It emphasizes conformal representations, the role of the RIEMANN surface, and the historic connections between RIEMANN, WEIERSTRASS, and other pioneers. The exposition introduces the exponential and trigonometric functions for complex arguments, including their addition theorems and fundamental relations, before turning to singularities, Laurent series, and the general theory of analytic continuation. A clear pathway is provided for readers who want both theoretical understanding and practical problem-solving tools.

• Foundational concepts: complex numbers, functions, and geometric representation
• Core theorems on regular and single-valued analytic functions
• Techniques in conformal mapping, rational and algebraic functions
• Expanded treatment of exponential, trigonometric, and multivalued functions

Ideal for readers of math and analysis who seek a compact, rigorous introduction to the theory of complex variables.

A propos du livre

Présentation de l'éditeur

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.)

About the Publisher

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

Présentation de l'éditeur

Excerpt from Theory of Functions of a Complex Variable

For a number of years there has been a feeling among many teachers of mathematics that students would accomplish more if they had an introductory treatise on the Theory of Functions of a Complex Variable written in English and adapted in other ways to the use of students beginning their graduate work. Professor Burkhardts book Einfuhrung in die Theorie der analytischen Funktionen einer komplexen Verdnderlichen 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, since there is no book in the English 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 figures and which follow various sections and each of the chapters, 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.

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

Détails de l'édition

• Éditeur: Forgotten Books
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 1440040362
• ISBN 13: 9781440040368
• Reliure: Broché
• Nombre de pages: 450
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