Calculus With Complex Numbers John B Reade Taylor Francis 2003 128S.pdf

Calculus plex Numbers
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Calculus with
Complex Numbers
John B. Reade
First published 2003
by Taylor & Francis
11 New Fetter Lane, London EC4P 4EE
Simultaneously published in the USA and Canada
by Taylor & Francis Inc.
29 West 35th Street, New York, NY 10001
Taylor & Francis is an imprint of the Taylor & Francis Group
This edition published in the Taylor & Francis e-Library, 2004.
© 2003 Taylor & Francis
All rights reserved. No part of this book may be reprinted or
reproduced or utilised in any form or by any electronic,
mechanical, or other means, now known or hereafter
invented, including photocopying and recording, or in any
information storage or retrieval system, without permission in
writing from the publishers.
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Cataloging in Publication Data
A catalog record for this book has been requested
ISBN 0-203-41786-0 Master e-book ISBN
ISBN 0-203-41934-0 (Adobe eReader Format)
ISBN 0–415–30846–1 (hbk)
ISBN 0–415–30847–X (pbk)
Contents
Preface vii
plex numbers 1
plex functions 14
3 Derivatives 24
4 Integrals 36
5 Evaluation of finite real integrals 49
6 Evaluation of infinite real integrals 53
7 Summation of series 65
8 Fundamental theorem of algebra 75
Solutions to examples 82
Appendix 1: Cauchy’s theorem 93
Appendix 2: Half residue theorem 95
Bibliography 97
Index of symbols and abbreviations 98
General index 99
Preface
This book is based on the premise that the learning curve is isomorphic to the
historical curve. In other words, the learning order of events is the same as the
historical order of events. For example, we learn arithmetic before we learn algebra.
We learn how before we learn why.
Historically, calculus with real numbers came first, initiated by Newton and
Leibnitz in the seventeenth century. Even plex numbers had been
known abou