Holdings: Generalized vector and dyadic analysis

Generalized vector and dyadic analysis: applied mathematics in field theory

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Bibliographic Details
Main Author:	Tai, Chen-To (Author)
Format:	Book
Language:	English
Published:	New York IEEE Press <<[u.a.]>> 1997
Edition:	2. ed.
Subjects:	Vektoranalysis
Online Access:	Inhaltsverzeichnis
ISBN:	0780334132

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MARC


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Record in the Search Index

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adam_text	GENERALIZED VECTOR AND DYADIC ANALYSIS APPLIED MATHEMATICS IN FIELD THEORY SECOND EDITION CHEN-TO TAI PROFESSOR EMERITUS RADIATION LABORATORY DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE UNIVERSITY OF MICHIGAN IEEE ANTENNAS & PROPAGATION SOCIETY, SPONSOR IEEE PRESS THE INSTITUTE OF ELECTRICAL OXFORD UNIVERSITY PRESS AND ELECTRONICS ENGINEERS, INC. OXFORD, TOKYO, NEW YORK MELBOURNE CONTENTS PREFACE TO THE SECOND EDITION XI PREFACE TO THE FIRST EDITION XIII ACKNOWLEDGMENTS FOR THE FIRST EDITION XV 1 VECTOR AND DYADIC ALGEBRA 1 1-1 REPRESENTATIONS OF VECTOR FUNCTIONS 1 1-2 PRODUCTS AND IDENTITIES 4 1-3 ORTHOGONAL TRANSFORMATION OF VECTOR FUNCTIONS 8 1-4 TRANSFORM OF VECTOR PRODUCTS 14 1-5 DEFINITION OF DYADICS AND TENSORS 16 1-6 CLASSIFICATION OF DYADICS 17 1-7 PRODUCTS BETWEEN VECTORS AND DYADICS 19 2 COORDINATE SYSTEMS 23 2-1 GENERAL CURVILINEAR SYSTEM (GCS) 23 2-2 ORTHOGONAL CURVILINEAR SYSTEM (OCS) 28 VII VIII CONTENTS 2-3 DERIVATIVES OF UNIT VECTORS IN OCS 33 2-4 DUPIN COORDINATE SYSTEM 35 2-5 RADII OF CURVATURE 37 3 LINE INTEGRALS, SURFACE INTEGRALS, AND VOLUME INTEGRALS 43 3-1 DIFFERENTIAL LENGTH, AREA, AND VOLUME 43 3-2 CLASSIFICATION OF LINE INTEGRALS 44 3-3 CLASSIFICATION OF SURFACE INTEGRALS 48 3-4 CLASSIFICATION OF VOLUME INTEGRALS 56 4 VECTOR ANALYSIS IN SPACE 58 4-1 SYMBOLIC VECTOR AND SYMBOLIC VECTOR EXPRESSIONS 58 4-2 DIFFERENTIAL FORMULAS OF THE SYMBOLIC EXPRESSION IN THE ORTHOGONAL CURVILINEAR COORDINATE SYSTEM FOR GRADIENT, DIVERGENCE, AND CURL 61 4-3 INVARIANCE OF THE DIFFERENTIAL OPERATORS 65 4-4 DIFFERENTIAL FORMULAS OF THE SYMBOLIC EXPRESSION IN THE GENERAL CURVILINEAR SYSTEM 69 4-5 ALTERNATIVE DEFINITIONS OF GRADIENT AND CURL 75 4-6 THE METHOD OF GRADIENT 78 4-7 SYMBOLIC EXPRESSIONS WITH TWO FUNCTIONS AND THE PARTIAL SYMBOLIC VECTORS 81 4-8 SYMBOLIC EXPRESSIONS WITH DOUBLE SYMBOLIC VECTORS 86 4-9 GENERALIZED GAUSS THEOREM IN SPACE 91 4-10 SCALAR AND VECTOR GREEN S THEOREMS 93 4-11 SOLENOIDAL VECTOR, IRROTATIONAL VECTOR, AND POTENTIAL FUNCTIONS 95 5 VECTOR ANALYSIS ON SURFACE 99 5-1 SURFACE SYMBOLIC VECTOR AND SYMBOLIC EXPRESSION FOR A SURFACE 99 5-2 SURFACE GRADIENT, SURFACE DIVERGENCE, AND SURFACE CURL 101 5-2-1 SURFACE GRADIENT 101 CONTENTS IX 5-2-2 SURFACE DIVERGENCE 102 5-2-3 SURFACE CURL 103 5-3 RELATIONSHIP BETWEEN THE VOLUME AND SURFACE SYMBOLIC EXPRESSIONS 104 5-4 RELATIONSHIP BETWEEN WEATHERBURN S SURFACE FUNCTIONS AND THE FUNCTIONS DEFINED IN THE METHOD OF SYMBOLIC VECTOR 104 5-5 GENERALIZED GAUSS THEOREM FOR A SURFACE 106 5-6 SURFACE SYMBOLIC EXPRESSIONS WITH A SINGLE SYMBOLIC VECTOR AND TWO FUNCTIONS 111 5-7 SURFACE SYMBOLIC EXPRESSIONS WITH TWO SURFACE SYMBOLIC VECTORS AND A SINGLE FUNCTION 113 6 VECTOR ANALYSIS OF TRANSPORT THEOREMS 116 6-1 HELMHOLTZ TRANSPORT THEOREM 116 6-2 MAXWELL THEOREM AND REYNOLDS TRANSPORT THEOREM 119 DYADIC ANALYSIS 121 7-1 DIVERGENCE AND CURL OF DYADIC FUNCTIONS AND GRADIENT OF VECTOR FUNCTIONS 121 7-2 DYADIC INTEGRAL THEOREMS 124 8 A HISTORICAL STUDY OF VECTOR ANALYSIS 127 8-1 INTRODUCTION 127 8-2 NOTATIONS AND OPERATORS 129 8-2-1 PAST AND PRESENT NOTATIONS IN VECTOR ANALYSIS 129 8-2-2 QUATERNION ANALYSIS 131 8-2-3 OPERATORS 132 8-3 THE PIONEER WORKS OF J. WILLARD GIBBS (1839-1903) 135 8-3-1 TWO PAMPHLETS PRINTED IN 1881 AND 1884 135 8-3-2 DIVERGENCE AND CURL OPERATORS AND THEIR NEW NOTATIONS 138 8-4 BOOK BY EDWIN BIDWELL WILSON FOUNDED UPON THE LECTURES OF J. WILLARD GIBBS 141 CONTENTS 8-4-1 GIBBS S LECTURE NOTES 141 8-4-2 WILSON S BOOK 141 8-4-3 THE SPREAD OF THE FORMAL SCALAR PRODUCT (FSP) AND FORMAL VECTOR PRODUCT (FVP) 146 8-5 V IN THE HANDS OF OLIVER HEAVISIDE (1850-1925) 149 8-6 SHILOV S FORMULATION OF VECTOR ANALYSIS 151 8-7 FORMULATIONS IN ORTHOGONAL CURVILINEAR SYSTEMS 152 8-7-1 TWO EXAMPLES FROM THE BOOK BY MOON AND SPENCER 152 8-7-2 A SEARCH FOR THE DIVERGENCE OPERATOR IN ORTHOGONAL CURVILINEAR COORDINATE SYSTEMS 154 8-8 THE USE OF V TO DERIVE VECTOR IDENTITIES 155 8-9 A RECASTING OF THE PAST FAILURES BY THE METHOD OF S Y MBOLIC VECTOR 157 8-9-1 IN RETROSPECT 159 APPENDIX A APPENDIX B APPENDIX C APPENDIX D APPENDIX E APPENDIX F REFERENCES INDEX 189 TRANSFORMATION BETWEEN UNIT VECTORS 161 VECTOR AND DYADIC IDENTITIES 165 INTEGRAL THEOREMS 169 RELATIONSHIPS BETWEEN INTEGRAL THEOREMS 170 VECTOR ANALYSIS IN THE SPECIAL THEORY OF RELATIVITY 174 COMPARISON OF THE NOMENCLATURES AND NOTATIONS OF THE QUANTITIES USED IN THIS BOOK AND IN THE BOOK BYSTRATTON 181 185
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author	Tai, Chen-To
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spelling	Tai, Chen-To Verfasser aut Generalized vector and dyadic analysis applied mathematics in field theory Chen-To Tai 2. ed. New York IEEE Press <<[u.a.]>> 1997 txt rdacontent n rdamedia nc rdacarrier Vektoranalysis (DE-588)4191992-0 gnd rswk-swf Vektoranalysis (DE-588)4191992-0 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018430507&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Tai, Chen-To Generalized vector and dyadic analysis applied mathematics in field theory Vektoranalysis (DE-588)4191992-0 gnd
subject_GND	(DE-588)4191992-0
title	Generalized vector and dyadic analysis applied mathematics in field theory
title_auth	Generalized vector and dyadic analysis applied mathematics in field theory
title_exact_search	Generalized vector and dyadic analysis applied mathematics in field theory
title_full	Generalized vector and dyadic analysis applied mathematics in field theory Chen-To Tai
title_fullStr	Generalized vector and dyadic analysis applied mathematics in field theory Chen-To Tai
title_full_unstemmed	Generalized vector and dyadic analysis applied mathematics in field theory Chen-To Tai
title_short	Generalized vector and dyadic analysis
title_sort	generalized vector and dyadic analysis applied mathematics in field theory
title_sub	applied mathematics in field theory
topic	Vektoranalysis (DE-588)4191992-0 gnd
topic_facet	Vektoranalysis
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018430507&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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