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Synopsis
This text is an attempt to cover some of the salient features of variable complex function theory. The approach is analytical, as opposed to geometric, but the methods of the three principal schools (Cauchy, Riemann and Weierstrass) are developed. The book goes into several topics deeply (eg, convergence theory and plane topology) and chapter notes give the sources of the results, trace lines of subsequent development, make connections with other topics, and offer suggestions for further reading. These notes are keyed to a bibliography of over 1300 books and papers.
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Review
"This is, I believe, the first modern comprehensive treatise on its subject. The author appears to have read everything, he proves everything, and he has brought to light many interesting but generally forgotten results and methods. The book should be on the desk of everyone who might ever want to see a proof of anything from the basic theory...." (SIAM Review)
" ... An attractive, ingenious, and many time[s] humorous form increases the accessibility of the book...." (Zentralblatt für Mathematik)
"Professor Burckel is to be congratulated on writing such an excellent textbook.... this is certainly a book to give to a good student [who] would profit immensely from it...." (Bulletin London Mathematical Society)
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- PublisherBirkhauser Verlag AG
- Publication date1979
- ISBN 10 376430989X
- ISBN 13 9783764309893
- BindingHardcover
- LanguageEnglish
- Number of pages558
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An Introduction to Classical Complex Analysis: Vol. 1 (Lehrbücher und Monographien aus dem Gebiete der exakten Wissenschaften, Band 64)
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An Introduction to Classical Complex Analysis : Vol. 1
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Introduction to Classical Complex Analysis
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Introduction to Classical Complex Analysis
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An Introduction to Classical Complex Analysis: Vol. 1 (Lehrbücher und Monographien aus dem Gebiete der exakten Wissenschaften, 64)
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An Introduction to Classical Complex Analysis. Vol.1
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Springer, Basel, Birkhäuser Basel, Birkhäuser Jan 1979, 1979
ISBN 10: 376430989X
ISBN 13: 9783764309893
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -to Classical Complex Analysis Vol. 1 by Robert B. Burckel Kansas State University 1979 BIRKHAUSER VERLAG BASEL UND STUTTGART CIP-Kurztitelaufnahme der Deutschen Bibliothek Burckel, Robert B.: An introduction to classical complex analysis I by Robert B. Burckel. - Basel. Stuttgart: Birkhiiuser. Vol. I. - 1979. (Lehrbilcher und Monographien aus dem Gebiete der exakten Wissenschaften: Math. Reihe; Bd. 64) All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the Copyright owner. Birkhiiuser Verlag Basel, 1979 North and South America Edition published by ACADEMIC PRESS. INC. III Fifth Avenue, New York, New York 10003 (Pure and Applied Mathematics, A Series of Monographs and Textbooks, Volume 82) ISBN-13: 978-3-0348-9376-3 e-ISBN-13: 978-3-0348-9374-9 DOl: 10.1007/978-3-0348-9374-9 Library of Congress Catalog Card Number 78-67403 5 Contents Volume I PREFACE 9 Chapter 0 PREREQUISITES AND PRELIMINARIES 131 Set Theory 132 Algebra 143 The Battlefield 144 Metric Spaces 155 Limsup and All That 186 Continuous Functions 207 Calculus 21 Chapter I CURVES, CONNECTEDNESS AND CONVEXITY 221 Elementary Results on Connectedness 222 Connectedness of Intervals, Curves and Convex Sets 233 The Basic Connectedness Lemma 284 Components and Compact Exhaustions 295 Connectivity of a Set 336 Extension Theorems 37 Notes to Chapter I 39 558 pp. Englisch. Seller Inventory # 9783764309893
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An Introduction to Classical Complex Analysis: Vol. 1 (Hardback or Cased Book)
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An Introduction to Classical Complex Analysis : Vol. 1
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - to Classical Complex Analysis Vol. 1 by Robert B. Burckel Kansas State University 1979 BIRKHAUSER VERLAG BASEL UND STUTTGART CIP-Kurztitelaufnahme der Deutschen Bibliothek Burckel, Robert B.: An introduction to classical complex analysis I by Robert B. Burckel. - Basel. Stuttgart: Birkhiiuser. Vol. I. - 1979. (Lehrbilcher und Monographien aus dem Gebiete der exakten Wissenschaften: Math. Reihe; Bd. 64) All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the Copyright owner. Birkhiiuser Verlag Basel, 1979 North and South America Edition published by ACADEMIC PRESS. INC. III Fifth Avenue, New York, New York 10003 (Pure and Applied Mathematics, A Series of Monographs and Textbooks, Volume 82) ISBN-13: 978-3-0348-9376-3 e-ISBN-13: 978-3-0348-9374-9 DOl: 10.1007/978-3-0348-9374-9 Library of Congress Catalog Card Number 78-67403 5 Contents Volume I PREFACE 9 Chapter 0 PREREQUISITES AND PRELIMINARIES 131 Set Theory 132 Algebra 143 The Battlefield 144 Metric Spaces 155 Limsup and All That 186 Continuous Functions 207 Calculus 21 Chapter I CURVES, CONNECTEDNESS AND CONVEXITY 221 Elementary Results on Connectedness 222 Connectedness of Intervals, Curves and Convex Sets 233 The Basic Connectedness Lemma 284 Components and Compact Exhaustions 295 Connectivity of a Set 336 Extension Theorems 37 Notes to Chapter I 39. Seller Inventory # 9783764309893
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Introduction to Classical Complex Analysis
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