A student's guide to vectors and tensors:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
[2012]
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | X, 197 Seiten Illustrationen |
| ISBN: | 9780521193696 9780521171908 |
Internformat
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| 245 | 1 | 0 | |a A student's guide to vectors and tensors |c Daniel A. Fleisch |
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| 264 | 4 | |c © 2012 | |
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Datensatz im Suchindex
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| adam_text | Titel: A student s guide to vectors and tensors
Autor: Fleisch, Daniel A
Jahr: 2012
Contents
Preface page vii
Acknowledgments x
1 Vectors 1
1.1 Definitions (basic) 1
1.2 Cartesian unit vectors 5
1.3 Vector components 7
1.4 Vector addition and multiplication by a scalar 11
1.5 Non-Cartesian unit vectors 14
1.6 Basis vectors 20
1.7 Chapter 1 problems 23
2 Vector operations 25
2.1 Scalar product 25
2.2 Cross product 27
2.3 Triple scalar product 30
2.4 Triple vector product 32
2.5 Partial derivatives 35
2.6 Vectors as derivatives 41
2.7 Nabla - the del operator 43
2.8 Gradient 44
2.9 Divergence 46
2.10 Curl 50
2.11 Laplacian 54
2.12 Chapter 2 problems 60
3 Vector applications 62
3.1 Mass on an inclined plane 62
3.2 Curvilinear motion 72
vi Contents
3.3 The electric field 81
3.4 The magnetic field 89
3.5 Chapter 3 problems 95
4 Covariant and contravariant vector components 97
4.1 Coordinate-system transformations 97
4.2 Basis-vector transformations 105
4.3 Basis-vector vs. component transformations 109
4.4 Non-orthogonal coordinate systems 110
4.5 Dual basis vectors 113
4.6 Finding covariant and contravariant components 117
4.7 Index notation 122
4.8 Quantities that transform contravariantly 124
4.9 Quantities that transform covariantly 127
4.10 Chapter 4 problems 130
5 Higher-rank tensors 132
5.1 Definitions (advanced) 132
5.2 Covariant, contravariant, and mixed tensors 134
5.3 Tensor addition and subtraction 135
5.4 Tensor multiplication 137
5.5 Metric tensor 140
5.6 Index raising and lowering 147
5.7 Tensor derivatives and Christoffel symbols 148
5.8 Covariant differentiation 153
5.9 Vectors and one-forms 156
5.10 Chapter 5 problems 157
6 Tensor applications 159
6.1 The inertia tensor 159
6.2 The electromagnetic field tensor 171
6.3 The Riemann curvature tensor 183
6.4 Chapter 6 problems 192
Further reading 194
Index 195
|
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| discipline | Physik Mathematik |
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| institution | BVB |
| isbn | 9780521193696 9780521171908 |
| language | English |
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| spelling | Fleisch, Daniel A. 1951- (DE-588)135640504 aut A student's guide to vectors and tensors Daniel A. Fleisch Cambridge Cambridge University Press [2012] © 2012 X, 197 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Tensor (DE-588)4184723-4 gnd rswk-swf Vektor (DE-588)4202708-1 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Vektor (DE-588)4202708-1 s DE-604 Tensor (DE-588)4184723-4 s Mathematische Physik (DE-588)4037952-8 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024153111&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fleisch, Daniel A. 1951- A student's guide to vectors and tensors Tensor (DE-588)4184723-4 gnd Vektor (DE-588)4202708-1 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4184723-4 (DE-588)4202708-1 (DE-588)4037952-8 |
| title | A student's guide to vectors and tensors |
| title_auth | A student's guide to vectors and tensors |
| title_exact_search | A student's guide to vectors and tensors |
| title_full | A student's guide to vectors and tensors Daniel A. Fleisch |
| title_fullStr | A student's guide to vectors and tensors Daniel A. Fleisch |
| title_full_unstemmed | A student's guide to vectors and tensors Daniel A. Fleisch |
| title_short | A student's guide to vectors and tensors |
| title_sort | a student s guide to vectors and tensors |
| topic | Tensor (DE-588)4184723-4 gnd Vektor (DE-588)4202708-1 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Tensor Vektor Mathematische Physik |
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