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Arfken-Solutions-Manual-7th-Ed.pdf

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Instructor’s Manual MATHEMATICAL METHODS FOR PHYSICISTS A Comprehensive Guide SEVENTH EDITION George B. Arfken Miami University Oxford, OH Hans J. Weber University of Virginia Charlottesville, VA Frank E. Harris University of Utah, Salt Lake City, UT; University of Florida, Gainesville, FL AMSTERDAM ã BOSTON ã HEIDELBERG ã LONDON NEW YORK ã OXFORD ã PARIS ã SAN DIEGO SAN FRANCISCO ã SINGAPORE ã SYDNEY ã TOKYO Academic Press is an imprint of Elsevier Academi
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  Instructor’s Manual  MATHEMATICALMETHODS FORPHYSICISTS A Comprehensive Guide SEVENTH EDITION George B. ArfkenMiami UniversityOxford, OHHans J. WeberUniversity of VirginiaCharlottesville, VAFrank E. HarrisUniversity of Utah, Salt Lake City, UT;University of Florida, Gainesville, FL AMSTERDAM  ã  BOSTON  ã  HEIDELBERG  ã  LONDONNEW YORK  ã  OXFORD  ã  PARIS  ã  SAN DIEGOSAN FRANCISCO  ã  SINGAPORE  ã  SYDNEY  ã  TOKYO Academic Press is an imprint of Elsevier  Academic Press is an imprint of Elsevier225 Wyman Street, Waltham, MA 02451, USAThe Boulevard, Langford Lane, Kidlington, Oxford, OX5 1GB, UK c  2013 Elsevier Inc. All rights reserved. No 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. 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: www.elsevier.com/permissions.This book and the individual contributions contained in it are protected undercopyright by the Publisher (other than as may be noted herein). Notices Knowledge 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 necessary.Practitioners 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 responsibility.To 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 herein.For information on all Academic Press publications,visit our website: www.books.elsevier.com  Contents 1 Introduction  1 2 Errata and Revision Status  3 3 Exercise Solutions  7 1. Mathematical Preliminaries . . . . . . . . . . . . . . . . . . . 72. Determinants and Matrices . . . . . . . . . . . . . . . . . . . . 273. Vector Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 344. Tensors and Differential Forms . . . . . . . . . . . . . . . . . . 585. Vector Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 666. Eigenvalue Problems . . . . . . . . . . . . . . . . . . . . . . . 817. Ordinary Differential Equations . . . . . . . . . . . . . . . . . 908. Sturm-Liouville Theory . . . . . . . . . . . . . . . . . . . . . . 1069. Partial 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 . . . . . . . . . . . . . . . . . . . . . 387 4 Correlation, Exercise Placement  398 5 Unused Sixth Edition Exercises  425 iv  Chapter 1 Introduction The seventh edition of   Mathematical Methods for Physicists   is 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. 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 material.Complete methods of solution have been provided for all the problems thatare new to this seventh edition. 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 problems.Not 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 ã  A new chapter (designated 31) on Periodic Systems, dealing with mathe-matical topics associated with lattice summations and band theory, ã  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

Fuzzy System

Jul 24, 2017
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