Mathematical-Methods-for-Physicists-a-Comprehensive-Guide-Arfken-Weber-Harris-7-Ed

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ArfKen_FM-9780123846549.tex
MATHEMATICAL
METHODS FOR
PHYSICISTS
SEVENTH EDITION
ArfKen_FM-9780123846549.tex
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
and
University of Florida, Gainesville, FL
AMSTERDAM BOSTON HEIDELBERG LONDON
NEW YORK OXFORD PARIS SAN DIEGO
SAN FRANCISCO SINGAPORE SYDNEY TOKYO
Academic Press is an imprint of Elsevier
ArfKen_FM-9780123846549.tex
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Knowledge and best practice in this field are constantly changing. As new research and experience
broaden our understanding, changes in research methods, professional practices, or medical treatment
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Practitioners and researchers must always rely on their own experience and knowledge in evaluating and
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To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any
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v
CONTENTS
PREFACE...........................................................................................................................................XI
1.MATHEMATICALPRELIMINARIES......................................................................................................1
1.1.InfiniteSeries..................................................................................................................1
1.2.SeriesofFunctions.......................................................................................................21
1.3.BinomialTheorem........................................................................................................33
1.4.MathematicalInduction...............................................................................................40
1.5.OperationsofSeriesExpansionsofFunctions..............................................................41
1.6.SomeImportantSeries.................................................................................................45
1.7.Vectors.........................................................................................................................46
1.8.ComplexNumbersandFunctions.................................................................................53
1.9.DerivativesandExtrema..............................................................................................62
1.10.EvaluationofIntegrals.................................................................................................65
1.11.DiracDeltaFunctions...................................................................................................75
AdditionalReadings....................................................................................................82
2.DETERMINANTSANDMATRICES....................................................................................................83
2.1Determinants...............................................................................................................83
2.2Matrices.......................................................................................................................95
AdditionalReadings..................................................................................................121
3.VECTORANALYSIS....................................................................................................................123
3.1ReviewofBasicsProperties........................................................................................124
3.2Vectorin3‐DSpaces.................................................................................................126
3.3CoordinateTransformations......................................................................................133
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