Instructors Manual - Elsevier

1 instructor s ManualMATHEMATICALMETHODS FORPHYSICISTSA Comprehensive GuideSEVENTH EDITIONG eorge B. ArfkenMiami UniversityOxford, OHHans J. WeberUniversity of VirginiaCharlottesville, VAFrank E. HarrisUniversity of Utah, Salt Lake City, UT;University of Florida, Gainesville, FLAMSTERDAM BOSTON HEIDELBERG LONDONNEW YORK OXFORD PARIS SAN DIEGOSAN FRANCISCO SINGAPORE SYDNEY TOKYOA cademic Press is an imprint of ElsevierAcademic Press is an imprint of Elsevier225 Wyman Street, Waltham, MA 02451, USAThe Boulevard, Langford Lane, Kidlington, Oxford, OX5 1GB, UKc 2013 Elsevier Inc. All rights part of this publication may be reproduced or transmitted in any form orby any means, electronic or mechanical, including photocopying, recording, orany information storage and retrieval system, without permission in writingfrom the publisher.

2 Details on how to seek permission and further informationabout the Publishers permissions policies and our arrangements with organi-zations such as the Copyright Clearance Center and the Copyright LicensingAgency, can be found at our website: book and the individual contributions contained in it are protected undercopyright by the Publisher (other than as may be noted herein).NoticesKnowledge and best practice in this field are constantly changing. As newresearch and experience broaden our understanding, changes in research meth-ods, professional practices, or medical treatment may become and researchers must always rely on their own experience andknowledge in evaluating and using any information, methods, compounds,or experiments described herein. In using such information or methods theyshould be mindful of their own safety and the safety of others, includingparties for whom they have a professional the fullest extent of the law, neither the Publisher nor the authors, con-tributors, or editors, assume any liability for any injury and/or damage topersons or property as a matter of products liability, negligence or otherwise,or from any use or operation of any methods, products, instructions, or ideascontained in the material information on all Academic Press publications,visit our website: Introduction12 Errata and Revision Status33 Exercise Preliminaries.

3 And Matrices .. Analysis .. and Differential Forms .. Spaces .. Problems .. Differential Equations .. Theory .. Differential Equations ..11110. Green s Functions ..11811. Complex Variable Theory ..12212. Further Topics in Analysis ..15513. Gamma Function ..16614. Bessel Functions ..19215. Legendre Functions ..23116. Angular Momentum ..25617. Group Theory ..26818. More Special Functions ..28619. Fourier Series ..32320. Integral Transforms ..33221. Integral Equations ..36422. Calculus of Variations ..37323. Probability and Statistics ..3874 Correlation, Exercise Placement3985 Unused Sixth Edition Exercises425ivChapter 1 IntroductionThe seventh edition ofMathematical Methods for Physicistsis a substantial anddetailed revision of its predecessor. The changes extend not only to the topicsand their presentation, but also to the exercises that are an important partof the student experience.

4 The new edition contains 271 exercises that werenot in previous editions, and there has been a wide-spread reorganization of thepreviously existing exercises to optimize their placement relative to the materialin the text. Since many Instructors who have used previous editions of this texthave favorite problems they wish to continue to use, we are providing detailedtables showing where the old problems can be found in the new edition, andconversely, where the problems in the new edition came from. We have includedthe full text of every problem from the sixth edition that was not used in thenew seventh edition. Many of these unused exercises are excellent but had tobe left out to keep the book within its size limit. Some may be useful as testquestions or additional study methods of solution have been provided for all the problems thatare new to this seventh edition.

5 This feature is useful to teachers who want todetermine, at a glance, features of the various exercises that may not be com-pletely apparent from the problem statement. While many of the problems fromthe earlier editions had full solutions, some did not, and we were unfortunatelynot able to undertake the gargantuan task of generating full solutions to nearly1400 part of this instructor s Manual but available from Elsevier s on-lineweb site are three chapters that were not included in the printed text but whichmay be important to some Instructors . These include A new chapter (designated 31) on Periodic Systems, dealing with mathe-matical topics associated with lattice summations and band theory, A chapter (32) on Mathieu functions, built using material from two chap-ters in the sixth edition, but expanded into a single coherent presentation,and1 CHAPTER 1.

6 INTRODUCTION2 A chapter (33) on Chaos, modeled after Chapter 18 of the sixth editionbut carefully addition, also on-line but external to this Manual , is a chapter (designated1) on Infinite Series that was built by collection of suitable topics from variousplaces in the seventh edition text. This alternate Chapter 1 contains no materialnot already in the seventh edition but its subject matter has been packaged intoa separate unit to meet the demands of Instructors who wish to begin theircourse with a detailed study of Infinite Series in place of the new MathematicalPreliminaries this instructor s Manual exists only on-line, there is an opportunityfor its continuing updating and improvement, and for communication, throughit, of errors in the text that will surely come to light as the book is used. Theauthors invite users of the text to call attention to errors or ambiguities, andit is intended that corrections be listed in the chapter of this Manual entitledErrata and Revision Status.

7 Errata and comments may be directed to the au-thors atharris at to the publisher. If users choose to forwardadditional materials that are of general use to Instructors who are teaching fromthe text, they will be considered for inclusion when this Manual is of this instructor s Manual has been greatly facilitated by theefforts of personnel at Elsevier . We particularly want to acknowledge the assis-tance of our Editorial Project Manager, Kathryn Morrissey, whose attention tothis project has been extremely valuable and is much is our hope that this instructor s Manual will have value to those whoteach fromMathematical Methods for Physicistsand thereby to their 2 Errata and Revision StatusLast changed: 25 June 2013 Errata and Comments re Seventh Edition textPage 165 Eq. ( )Interchangeuandv, to read (v u) =v 2u+ ( u) ( v).

8 Page 287 Eq. ( )Rightmost member should read c .Page 292 4 lines after Eq. ( ) The first sum should be over index .Page 319 Last paragraphFirst sentence should read as for Hermitianmatrices. Page 522 Exercise (a)This is not a principal-value 535 Figure two arrowheads in the lower part of thecircular arc should be reversed in 539 Exercise answer is incorrect; it should be 585 Exercise the integral for which a series is soughtto 0e xv1 +v2dv. The answer is then 610 Exercise ( t) bye i t .Page 615 Exercise the Hint, change Eq. ( ) to Eq. ( ).Page 618 Eq. ( )Change toB(p+ 1,q+ 1).3 CHAPTER 2. ERRATA AND REVISION STATUS4 Page 624 After Eq. ( )C1can be determined by requiring consistencywith the recurrence formulaz (z) = (z+ 1).Consistency with the duplication formula 625 Exercise (see Fig.)

9 By and that of therecurrence formula .Page 660 Exercise that 2= 2/c2, where is the angularfrequency, and that the height of the cavity 664 Eq. ( )The integral lacks the differentiald .Page 665 Exercise Eq. ( ) to Eq. ( ).Page 686 Exercise part (b), changeltohin the formulas foramnandbmn(denominator and integrationlimit).Page 687 Exercise indexnis assumed to be an 695 Exercise indexnis assumed to be an 696 Exercise (b)ChangeNtoY(two occurrences).Page 709 Exercise the summation preceded by the cosinefunction, change (2z)2sto (2z)2s+ 710 Exercise (x) byyn(x).Page 723 Exercise last formula of the answer should readP2s(0)/(2s+ 2) = ( 1)s(2s 1)!!/(2s+ 2)!!.Page 754 Exercise minus sign beforeP1n(cos ).Page 760 Table 13, change font:costo 877 Exercise both (a) and (b), change 2 to 2.

10 Page 888 Exercise the second of the four members of thefirst display equation to(x+ip 2) n(x), andchange the corresponding member of thesecond display equation to(x ip 2) n(x).Page 888 Exercise +iptox 893 Table 4!Lk4, insertx2after (k+ 3)2andxafter (k+ 2) 909 Exercise instances ofxshould be 910 Exercise text does not state that theT0term (ifpresent) has an additional factor 1 2. ERRATA AND REVISION STATUS5 Page 911 Exercise (b) The ratio approaches ( s) 1/2, not ( s) 915 Exercise hypergeometric function should read2F1( 2+12, 2+ 1; +32;z 2).Page 916 Exercise (n 12)! to (n+12).Page 916 Exercise be an 917 Eq. ( )In the last term change ( c) to (2 c).Page 921 Exercise (two occurrences).Page 931 Exercise arguments 932 Exercise arguments ofKandEarek2; in theintegrand of the hint, 943 Last line of textChange figure reference to Fig.