Vectors and tensors in engineering and physics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Reading, Mass. u.a.
Addison-Wesley
1997
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | V, 282 S. graph. Darst. |
| ISBN: | 0201442108 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804125948201664512 |
|---|---|
| adam_text | CONTENTS
PREFACE v
1 VECTOR ALGEBRA 1
1.1 INTRODUCTION 1
1.2 HISTORICAL NOTES 1
1.3 VECTOR BASICS 2
1.4 DOT AND CROSS PRODUCT 5
1.5 PHYSICAL SCALARS AND VECTORS 9
1.6 NOTATION OF OTHERS 16
2 TENSOR ALGEBRA 17
2.1 TENSORS DEFINED 17
2.2 BASIC PROPERTIES OF TENSORS 20
2.3 MORE PROPERTIES OF SECOND ORDER TENSORS 22
2.4 PHYSICAL TENSORS 24
2.5 NOTATION OF OTHERS 28
3 CARTESIAN COMPONENTS 29
3.1 COMPONENTS 29
3.2 TENSOR COMPONENTS 34
3.3 EIGENVECTOR REPRESENTATIONS 36
3.4 GEOMETRIC DISTORTIONS AND THE POLAR
DECOMPOSITION THEOREM 42
3.5 PHYSICAL APPLICATIONS 45
3.6 NOTATION OF OTHERS 50
4 GENERAL COMPONENTS 51
4.1 CHANGE OF CARTESIAN BASE VECTORS AND
COORDINATE SYSTEMS 51
4.2 ROTATIONS IN TWO DIMENSIONS 55
4.3 ROTATIONS IN THREE DIMENSIONS 60
4.4 INVARIANCE OF TENSOR COMPONENTS 62
4.5 GENERAL BASES 67
4.6 NOTATION OF OTHERS 71
5 TENSOR FIELDS OF ONE VARIABLE 73
5.1 BASIC CALCULUS OF VECTOR FIELDS 73
5.2 MOVING BASE VECTORS 75
5.3 NEWTONIAN MECHANICS OF A PARTICLE 78
5.4 DIFFERENTIAL GEOMETRY OF A SPACE CURVE 84
5.5 MOTION OF A RIGID BODY 88
5.6 NOTATION OF OTHERS 97
iii
iv Contents
6 TENSOR FIELDS 99
6.1 DIFFERENTIATION OF SCALAR FIELDS 99
6.2 DIFFERENTIATION OF VECTOR FIELDS 104
6.3 LINE, SURFACE, AND VOLUME INTEGRALS 108
6.4 GREEN S THEOREM AND POTENTIAL FIELDS OF
TWO VARIABLES 113
6.5 STOKES AND DIVERGENCE THEOREMS AND POTENTIAL
FIELDS OF THREE VARIABLES 122
6.6 NOTATION OF OTHERS 129
7 APPLICATIONS 131
7.1 HEAT CONDUCTION 131
7.2 SOLID MECHANICS 138
7.3 FLUID MECHANICS 148
7.4 NEWTONIAN ORBITAL MECHANICS 157
7.5 ELECTROMAGNETIC THEORY 164
7.6 NOTATION OF OTHERS 176
8 GENERAL COORDINATES 177
8.1 GENERAL CURVILINEAR COORDINATES 177
8.2 ORTHOGONAL CURVILINEAR COORDINATES 184
8.3 SURFACE COORDINATES 191
8.4 MECHANICS OF CURVED MEMBRANES 200
8.5 NOTATION OF OTHERS 205
9 FOUR DIMENSIONAL SPACETIME 207
9.1 SPECIAL RELATIVITY 207
9.2 GENERAL RELATIVITY 216
9.3 NOTATION OF OTHERS 222
REFERENCES 225
HISTORICAL 225
MATHEMATICAL 225
PHYSICAL 227
ANSWERS TO PROBLEMS 231
INDEX 275
|
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)35636980 (DE-599)BVBBV011432817 |
| dewey-full | 530.1/5563 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
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| dewey-search | 530.1/5563 |
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| discipline | Physik Technik Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-09T18:09:40Z |
| institution | BVB |
| isbn | 0201442108 |
| language | English |
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| physical | V, 282 S. graph. Darst. |
| publishDate | 1997 |
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| spelling | Danielson, Donald A. Verfasser aut Vectors and tensors in engineering and physics D. A. Danielson 2. ed. Reading, Mass. u.a. Addison-Wesley 1997 V, 282 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Calculus of tensors Vektor (DE-588)4202708-1 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Ingenieurwissenschaften (DE-588)4137304-2 gnd rswk-swf Tensor (DE-588)4184723-4 gnd rswk-swf Tensor (DE-588)4184723-4 s Ingenieurwissenschaften (DE-588)4137304-2 s 1\p DE-604 Vektor (DE-588)4202708-1 s 2\p DE-604 Physik (DE-588)4045956-1 s 3\p DE-604 4\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007688369&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Danielson, Donald A. Vectors and tensors in engineering and physics Calculus of tensors Vektor (DE-588)4202708-1 gnd Physik (DE-588)4045956-1 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Tensor (DE-588)4184723-4 gnd |
| subject_GND | (DE-588)4202708-1 (DE-588)4045956-1 (DE-588)4137304-2 (DE-588)4184723-4 |
| title | Vectors and tensors in engineering and physics |
| title_auth | Vectors and tensors in engineering and physics |
| title_exact_search | Vectors and tensors in engineering and physics |
| title_full | Vectors and tensors in engineering and physics D. A. Danielson |
| title_fullStr | Vectors and tensors in engineering and physics D. A. Danielson |
| title_full_unstemmed | Vectors and tensors in engineering and physics D. A. Danielson |
| title_short | Vectors and tensors in engineering and physics |
| title_sort | vectors and tensors in engineering and physics |
| topic | Calculus of tensors Vektor (DE-588)4202708-1 gnd Physik (DE-588)4045956-1 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Tensor (DE-588)4184723-4 gnd |
| topic_facet | Calculus of tensors Vektor Physik Ingenieurwissenschaften Tensor |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007688369&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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