Complex Variables and Applications (z-lib.org).pdf

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详细说明：复变函数与应用第九版英文版作者: ［美］詹姆斯·沃德·布朗等 (中文版当当上有卖)Brown and Churchill Series Comple r Variables and Applications. h edition Fourier Series and Bondan Vulue Pmblems. 8th edition The Walter rudin student series in advanced mathematics Bona. iklos: Intoduction 1o Enumerative Combinatorics Chartrand, Gary and Ping Zhang: Induc tion o Graph Theon Davis, Sheldon: Topology Rudin, Walter: Pr s of Mathematica/ Analy si. Rudin, Walter: Real and Comple r Anual sia Other mcfraw-Hill Titles in Higher mathematics Ahlfors, Lars: Comple. r Analvsis Burton David l. Elementan Number Theory Burton, David .. The Histon of Mathematic s: An /truction Hvidsten, Michael: Geometn w'ith Geometr r Explorer COMPLEX VARIABLES AND APPLICATIONS Ninth editi James Ward Brown Pmfessor Emmeritu.s of Mathematic:s The Uniersity of Michigan-Dearborn Ruel v churchill ate Professorof Mathematic s The Unier sirv'of Michhigan-Dearbor Mc Graw Education Mc Graw Education COMPLEXⅤR」 ABLES∧ NDAPPLICATIONS. NINTH EDITION Published by mcgraw Hill Education. 2 Penn Plaz a New York. NY 10)121. Copyright 201+ by MCGraw-Hill Education. All rights reserved. Printed in th lInited Siales of America. Previous editions o2()9. 2X)4.& 1996. No paut of uis publicalion may be reproduced or distributed in any Form or by any means. or stored in a diabase or retrieval system. w it lo)ut the prior written consent of Mc Graw-Hill Education. iNCluding, bul n)t limited to. in any new ork or other eleetronie storage oriransm ission ol broadcast tor distane learnin Some aIx illar ies iIk luding clec tronic and print components. may not he available to customers oulsic the l!nited stales This buk is printed on acid-tree paper 23456789()DQC'AC()98765↓3 LSBN978-007.338317-0 MHID().0738317 Senior vice president Produets makets: KurtLSrrenndl Vice Presickenl. General MilLger: Furn Lange Vice president. Content product ion Techology sevices: Kim/xr/ Meriis'ethierDur'iel Managing director: T/umas Timp Executive BraiN Manager: Bill Stein(isT Excculilc Marketing manager Curt rer/kels Developent editors: Loi'Taiine Buc-ek an Sitnthut 1 )nisi-1emnHI Director. Content Production T0rr'iSctieA/ Senior Project manager: Melixuci M. trick CoVer Iksigikr: Stdio mfmfuge St. Unis. MO Buver:/eier Pike l Media project Manager Sridevi Pikuni Compositor: APS Limiter Typeface: 10.25 x /2 Tine Rommel Printer:R.R melley All credits appearing on page or at the end of the book are con sidered to be an extension of the copy right page Library of Congress Cataloging-in-Publicat ion Data Churche‖!RueV.(RucⅤane,J8991987 Complex variables aix applications/ James Ward Brown. professor of mathenatics. Th U of Michigan/Dearborn Ruel v. churchill. late professor of malIemais. The Lfniversilvof Michiga., Ninth ilion Pages CIn Churchill s name appears hirst on tI eiliereuitions Includes bibliographical refereix'es and index sBN9780.073.38.3170(alk.,par 1. Functions of complex variables. I. Brown. James Wad. IL. Title Q31.7C242014 55.9d23 2(318657 The Internet addresses listed in the lext were acc urale al the tie of publication. The illusion of a website dos not indicale ann endorsement by thk author s or McGraw -Hill education. auld Mc graw-Hill Education des lol guaranlee the accuracy of the informition presened al diese siles Www. mhhe. coll ABOUT THE AUTHORS JAMES WARD BROWN is Prolessor emeritus of mathe matics at The university ol Michigan-De arbor. He eamed his A B in physics from Harvard University and his A.M. and Ph. D in mathematics from The University of Michigan in Ann Arbor, where he was an Institule of science and Technology predoctoral fellow. he is coauthor with Dr. Churchill of fourier Series and Bowdon Value problems, now in its eighth edition He has received a research grant from the nalional science foundation as well as a Distinguished Faculty Award fron the Michigan Association of Goveming Boards ol Colleges and universities. Dr. Brown is listed in Whos Wio in the world RUEL V. CHURCHILL was at the (ime of his death in 1987. Professor emeritus ol Mahe maties al the universitv of michigan where he began teaching in 1922. he received his B.s. in physics Iron the University of Chicago and his M.s. in physics and Ph. D in mathematics from The University ol Michigan. He was coauthor with Dr Brown of Fourier Series and Bounden value problems, a c lassie lext that he first wrote almost 75 years agO. He was also the author of Operat/ Mathematic S. Dr. Churchill held various offices in the mathemalical Asscxialion of America and in other mathemalical societies and councils This pag e intentionally le/n blank TO THE MEMORY OF MY FATHER GLORGL H. BROWN AND OF MY LONG-TIME FRIEND AND COAUTHOR RUEL V. CHURCHILL THESE DISTINGUISHED MEN OF SCIENCE FOR YEARS INFLUENCED THE CAREERS OF MANY EOPLE INCLUDING MINE J. WB This pag e intentionally le/n blank CONTENTS Preface xy 1 Complex Numbers 1 Sus andl products I Basic Algebrac Properties 3 Further Algebrait Propenies 5 Ⅴ clon and moduli8 Triang le Ine oilily I Complex Conjugates 14 Exponential ForIm 17 Pnducts and Powers in Exponential for 20 Arguments of Products and Quotients 21 RaxIs of Complex Numbers 25 EX amples 28 Regions in the compplex plane 3? 2 Analytic Functions 37 Functions and Mappings 37 The mapping t 40 Limits 4 Theorems on Limi【s47 Limits Involving the point at Infinity 50 X

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