Tensor calculus:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Polish |
| Veröffentlicht: |
Amsterdam u.a.
Elsevier
1974
|
| Ausgabe: | 3. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 371 S. |
| ISBN: | 0444411240 |
Internformat
MARC
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| 240 | 1 | 0 | |a Rachunek tensorowy |
| 245 | 1 | 0 | |a Tensor calculus |c by Stanisław Gołąb |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Amsterdam u.a. |b Elsevier |c 1974 | |
| 300 | |a XVIII, 371 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Algebra Linear |2 larpcal | |
| 650 | 7 | |a Analise Vetorial |2 larpcal | |
| 650 | 7 | |a Tensoren |2 gtt | |
| 650 | 4 | |a Calculus of tensors | |
| 650 | 0 | 7 | |a Tensorrechnung |0 (DE-588)4192487-3 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804117094670794752 |
|---|---|
| adam_text | CONTENTS
From the Preface to the First Edition xi
From the Preface to the Second Edition xvi
Preface to the Third Edition xviii
PARTI. THE ALGEBRA OF TENSORS 2
Chapter I. Introductory Concepts 3
0. Introductory Remarks 3
1. Analytic Spaces 3
2. Groups and Subgroups 7
3. Two Points of View Concerning Transformations in Analytic Space . . 10
4. The Geometry of the Space Gr 13
5. Subgroups of the Group d 14
6. Linear Subspaces of the Space En 19
7. Choice of Notation 20
8. Points of Space. Coordinate Systems. Coordinates of a Point. Types
of Indices 21
Chapter II. Geometric Objects 30
9. Vectors. Contra variant Vectors 30
10. The Concept of Geometric Object 36
11. Covariant Vectors 41
12. The Geometric Interpretation of the Covariant Vector 44
13. The Mutual Relationship Between Contra- and Co-variant Vectors. . 48
14. Vector Algebra with the Pseudogroup G, 49
15. The Linear Dependence of Vectors 51
16. Basis Vectors 52
Chapter HI. Tensors and Tensor Algebra 58
17. The Concept of Tensor 58
18. The Unit Tensor 61
19. The Product of a Tensor with a Number a 63
20. The Sum of Tensors 64
21. Linear Dependence of Tensors 64
Viii CONTENTS
22. The Tensor Product 65
23. The Contraction of Tensors 66
24. Transvection of Tensors 67
25. Mixing, or Symmetrization of Indices 68
26. The Isomers of a Tensor 73
27. Skew (Antisymmetric) Tensors 75
28. Polyvectors (Multivectors) 76
29. Densities 82
30. The Geometric Interpretation of n-Vectors. Volume Measure .... 85
31. Space Orientation 88
32. The Algebra of Densities 90
33. Tensor Densities 93
34. Geometric Objects Other than Quantities 98
35. Conditions Sufficient for an Object to be a Tensor 99
36. The Basis (Fundamental) Tensor 101
37. The Operation of Raising and Lowering Indices 104
38. The Fundamental Tensor as a Metric Tensor 106
39. The Scalar Product 108
40. The Perpendicularity of Vectors 112
41. The Unit Vector of a Vector 113
42. The Geometric Interpretation of the Tensor gx^ 113
43. Ricci n-Vectors 116
44. Vector Products 117
45. The Canonical Form of the Fundamental Tensor 122
46. The Eigenvalues of a Tensor 124
Chapter IV. A Supplement to Tensor Algebra 127
47. Restriction of Groups and Type of Quantity 127
48. Another Definition of Tensors 129
49. Dyadics (Dual Sums) 131
50. Anholonomic Systems 133
51. The Object of Anholonomicity 140
52. The Hessian of a Scalar Field 145
53. Pentsov Objects 146
54. The Density Gradient 148
55. Split Tensors 149
56. Strong Quantities 154
57. Multipoint Tensor Fields 155
58. A Backward Glance 156
PART II. THE ANALYSIS OF TENSORS 161 ,
Chapter V. Parallel Displacement 163
59. The Derivative of a Vector Field Along a Curve. The Object of Con¬
nection 163
60. The Object / „ 174
CONTENTS ix
61. The Symmetric and Antisymmetric Parts of the Object of Connection 176
62. Other Ways of Introducing the Object of Parallel Displacement ... 178
63. Parallel Displacement in Riemannian Space 183
64. Another Way of Introducing the Object r$r 188
65. A System Moving Geodesically Along a Line 189
66. The Covariant Derivative 190
67. The Absolute Derivative of Other Quantities 191
68. The Derivative of the Unit Tensor 198
69. Geodesies of the Space Ln 199
70. Affine Parameter on a Curve 204
71. Locally Geodesic (Normal) Coordinates 208
72. Riemann s Normal Coordinates 211
Chapter VI. Curvature and Torsion Tensors 214
73. The Curvature Tensor 214
74. Another Way of Introducing the Curvature Tensor 217
75. Two-Fold Covariant Differentiation of a Density 218
76. The Torsion Tensor and its Interpretation 219
77. The Interpretation of the Curvature Tensor 221
78. Concomitants of the Curvature Tensor 224
79. A Geometric Interpretation of the Tensors V^ and Rxp 225
80. The Relations Between the Coordinates of the Curvature Tensor . . 229
81. The Bianchi Identity 231
Chapter VII. The Metric of Riemannian Space 237
82. Christoffel Symbols. Uniquely Distinguishing an Object of Linear Con¬
nection for Riemannian Space 237
83. The Properties of ChristofFel Symbols as an Object of Parallel Dis¬
placement 239
84. Tensors Constant Under Covariant Differentiation 242
85. Lengths and Angles Under Parallel Displacement 245
86. Metrization of a Space Equipped with a Linear Connection .... 246
Chapter VIII. Some Special Spaces 250
87. Affine-Euclidean Spaces. Teleparallelism 250
88. Metric-Euclidean Spaces 254
89. Ricci CoeflScients of Rotation 255
90. Weyl Spaces 258
91. Einstein Spaces 260
92. Spaces of Constant Curvature 262
93. Spaces of Recurrent Curvature 263
94. Projective-Euclidean Spaces 264
95. Conformal Transformations of Riemannian Space 268
96. Hermitian Spaces 275
97. Almost Complex Spaces 277
x CONTENTS
Chapter IX. Differential Operators and Integral Theorems ... 279
98. Invariant Differential Operators 279
99. The Integrability Conditions for Differential Tensor Fields 286
100. The Formulae of Green, Stokes, and Gauss-Ostrogradski 288
101. The Oriented Multiple Integral 289
102. Integral Formulae 292
PART HI. THE APPLICATIONS OF TENSOR CALCULUS . 297
Chapter X. The Applications of Tensor Calculus to Geometry . 299
103. Geodesic Lines as the Extremals of a Certain Variational Problem . 299
104. The Geometry of Embedded Spaces 304
105. A Hyperspace Kn_! Embedded in the Space Vn 310
106. Normal Geodesic Coordinates 312
107. The Curvature Vector. The Relative and Forced Curvature Vectors . 314
108. Asymptotic Lines 316
109. Spherical Points 317
110. Conjugate Directions 317
111. Curvature Lines 317
112. The Equations of Gauss and Mainardi-Codazzi 318
113. The Differential Parameters of Beltrami 320
114. The Frenet Equations 331
Chapter XI. Other Applications 338
115. The Lie Derivative 338
116. The Concept of Differentiable Manifold 344
117. Harmonic Tensors 346
Conclusion 348
Bibliography 349
A. Textbooks and Monographs 349
B. Specialized Works 352
List of Principal Formulae and Symbols 357
Author Index 363
Subject Index 366
|
| any_adam_object | 1 |
| author | Gołąb, Stanisław 1902-1980 |
| author_GND | (DE-588)13328333X |
| author_facet | Gołąb, Stanisław 1902-1980 |
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| author_variant | s g sg |
| building | Verbundindex |
| bvnumber | BV002741760 |
| callnumber-first | Q - Science |
| callnumber-label | QA433 |
| callnumber-raw | QA433 |
| callnumber-search | QA433 |
| callnumber-sort | QA 3433 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)1103981 (DE-599)BVBBV002741760 |
| dewey-full | 515/.63 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.63 |
| dewey-search | 515/.63 |
| dewey-sort | 3515 263 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV002741760 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:48:56Z |
| institution | BVB |
| isbn | 0444411240 |
| language | English Polish |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001753013 |
| oclc_num | 1103981 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-20 DE-29T DE-706 DE-91G DE-BY-TUM DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-20 DE-29T DE-706 DE-91G DE-BY-TUM DE-634 DE-83 DE-11 DE-188 |
| physical | XVIII, 371 S. |
| psigel | TUB-nvmb HUB-ZB011200906 |
| publishDate | 1974 |
| publishDateSearch | 1974 |
| publishDateSort | 1974 |
| publisher | Elsevier |
| record_format | marc |
| spelling | Gołąb, Stanisław 1902-1980 Verfasser (DE-588)13328333X aut Rachunek tensorowy Tensor calculus by Stanisław Gołąb 3. ed. Amsterdam u.a. Elsevier 1974 XVIII, 371 S. txt rdacontent n rdamedia nc rdacarrier Algebra Linear larpcal Analise Vetorial larpcal Tensoren gtt Calculus of tensors Tensorrechnung (DE-588)4192487-3 gnd rswk-swf Tensorrechnung (DE-588)4192487-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001753013&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gołąb, Stanisław 1902-1980 Tensor calculus Algebra Linear larpcal Analise Vetorial larpcal Tensoren gtt Calculus of tensors Tensorrechnung (DE-588)4192487-3 gnd |
| subject_GND | (DE-588)4192487-3 |
| title | Tensor calculus |
| title_alt | Rachunek tensorowy |
| title_auth | Tensor calculus |
| title_exact_search | Tensor calculus |
| title_full | Tensor calculus by Stanisław Gołąb |
| title_fullStr | Tensor calculus by Stanisław Gołąb |
| title_full_unstemmed | Tensor calculus by Stanisław Gołąb |
| title_short | Tensor calculus |
| title_sort | tensor calculus |
| topic | Algebra Linear larpcal Analise Vetorial larpcal Tensoren gtt Calculus of tensors Tensorrechnung (DE-588)4192487-3 gnd |
| topic_facet | Algebra Linear Analise Vetorial Tensoren Calculus of tensors Tensorrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001753013&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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