Real and Complex Analysis Volume 2
This is the second volume of the two-volume book on real and complex analysis. This volume is an introduction to the theory of holomorphic functions. Multivalued functions and branches have been dealt carefully with the application of the machinery of com
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Real and Complex Analysis Volume 2
Real and Complex Analysis
Rajnikant Sinha
Real and Complex Analysis Volume 2
123
Rajnikant Sinha Varanasi, Uttar Pradesh, India
ISBN 978-981-13-2885-5 ISBN 978-981-13-2886-2 https://doi.org/10.1007/978-981-13-2886-2
(eBook)
Library of Congress Control Number: 2018957649 © Springer Nature Singapore Pte Ltd. 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Preface
The book is an introduction to real and complex analysis that will be useful to undergraduate students of mathematics and engineering. It is designed to equip the reader with tools that will help them to understand the concepts of real analysis and complex analysis. In addition, it contains the essential topics of analysis that are needed for the study of functional analysis. Its guiding principles help develop the necessary concepts rigorously with enough detail and with the minimum prerequisites. Further, I have developed the necessary tools to enhance the readability. This book contains complete solutions to almost all the problems discussed within. This will be beneficial to readers only if used correctly: readers are encouraged to look at the solution to a problem only after trying to solve the problem. Certainly, at times, the reader may find the proofs excruciatingly detailed, but it is better to be detailed than concise. Furthermore, eliding over detailed calculation can sometimes be perplexing for the beginners. I have tried to make it a readable text that caters to a broad audience. This approach should certainly benefit beginners who have not yet tussled with the subject in a serious way. This book contains several useful theorems and their proofs in
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