Generalized vector and dyadic analysis: applied mathematics in field theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
IEEE Press <<[u.a.]>>
1997
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| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| ISBN: | 0780334132 |
Internformat
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Datensatz im Suchindex
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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
|
| any_adam_object | 1 |
| author | Tai, Chen-To |
| author_facet | Tai, Chen-To |
| author_role | aut |
| author_sort | Tai, Chen-To |
| author_variant | c t t ctt |
| building | Verbundindex |
| bvnumber | BV024453961 |
| classification_rvk | SK 350 SK 400 SK 600 |
| ctrlnum | (OCoLC)634623083 (DE-599)BVBBV024453961 |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-09T21:59:55Z |
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| isbn | 0780334132 |
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| publishDate | 1997 |
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| publisher | IEEE Press <<[u.a.]>> |
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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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