www.elsolucionario.net www.elsolucionario.net V e ~ d r = / B d a , (Gauss), L ( ~ x A ) d a = A-dl, (Stokes) S (@v2y?- y?v2@)d3r (@V@- y?V@) da, (Green) www.elsolucionario.net Cumed Orthogonal Coordinates I,'~jlinrlerCoordirtcr,les !%frttiemriticcrlChlzslcrntu e = 2.718281828, sr = 3.14159265, In 10 = 2.302585093, rad = 57.29577951°, lo= 0.0174532925 rad, (Euler-Mascheroni number) Bl = -2 1 &=g,B'=&=-&=30 ' 42' (Bernoulli numbers) "' www.elsolucionario.net MATHEMATICAL METHODS FOR PHYSICISTS SIXTH EDITION George B Arfken Miami University Oxford, OH Hans J Weber University of Virginia Charlottesville, VA Amsterdam Boston Heidelberg London New York Oxford Paris San Diego San Francisco Singapore Sydney Tokyo www.elsolucionario.net This page intentionally left blank www.elsolucionario.net MATHEMATICAL METHODS FOR PHYSICISTS SIXTH EDITION www.elsolucionario.net This page intentionally left blank www.elsolucionario.net Acquisitions Editor Project Manager Marketing Manager Cover Design Composition Cover Printer Interior Printer Tom Singer Simon Crump Linda Beattie Eric DeCicco VTEX Typesetting Services Phoenix Color The Maple–Vail Book Manufacturing Group Elsevier Academic Press 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA 525 B Street, Suite 1900, San Diego, California 92101-4495, USA 84 Theobald’s Road, London WC1X 8RR, UK This book is printed on acid-free paper ∞ Copyright © 2005, Elsevier Inc All rights reserved No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone: (+44) 1865 843830, fax: (+44) 1865 853333, e-mail: permissions@elsevier.co.uk You may also complete your request on-line via the Elsevier homepage (http://elsevier.com), by selecting “Customer Support” and then “Obtaining Permissions.” Library of Congress Cataloging-in-Publication Data Appication submitted British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN: 0-12-059876-0 Case bound ISBN: 0-12-088584-0 International Students Edition For all information on all Elsevier Academic Press Publications visit our Web site at www.books.elsevier.com Printed in the United States of America 05 06 07 08 09 10 www.elsolucionario.net CONTENTS Preface xi Vector Analysis 1.1 Definitions, Elementary Approach 1.2 Rotation of the Coordinate Axes 1.3 Scalar or Dot Product 1.4 Vector or Cross Product 1.5 Triple Scalar Product, Triple Vector Product 1.6 Gradient, ∇ 1.7 Divergence, ∇ 1.8 Curl, ∇× 1.9 Successive Applications of ∇ 1.10 Vector Integration 1.11 Gauss’ Theorem 1.12 Stokes’ Theorem 1.13 Potential Theory 1.14 Gauss’ Law, Poisson’s Equation 1.15 Dirac Delta Function 1.16 Helmholtz’s Theorem Additional Readings 1 12 18 25 32 38 43 49 54 60 64 68 79 83 95 101 Vector Analysis in Curved Coordinates and Tensors 2.1 Orthogonal Coordinates in R3 2.2 Differential Vector Operators 2.3 Special Coordinate Systems: Introduction 2.4 Circular Cylinder Coordinates 2.5 Spherical Polar Coordinates 103 103 110 114 115 123 v ... (Bernoulli numbers) "' www.elsolucionario.net MATHEMATICAL METHODS FOR PHYSICISTS SIXTH EDITION George B Arfken Miami University Oxford, OH Hans J Weber University of Virginia Charlottesville,... blank www.elsolucionario.net PREFACE Through six editions now, Mathematical Methods for Physicists has provided all the mathematical methods that aspirings scientists and engineers are likely to... hold for rotations because they preserve volumes For a more general orthogonal transformation, the r.h.s of Eqs (1.46) is multiplied by the determinant of the transformation matrix (see Chapter for