Tensors and manifolds: with applications to physics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2009
|
| Ausgabe: | 2. ed., 1. publ. in paperback |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XIV, 447 S. graph. Darst. |
| ISBN: | 9780199564828 9780198510598 |
Internformat
MARC
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| 100 | 1 | |a Wasserman, Robert H. |d 1926- |e Verfasser |0 (DE-588)1013629124 |4 aut | |
| 245 | 1 | 0 | |a Tensors and manifolds |b with applications to physics |c Robert H. Wasserman |
| 250 | |a 2. ed., 1. publ. in paperback | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2009 | |
| 300 | |a XIV, 447 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Calculus of tensors | |
| 650 | 4 | |a Manifolds (Mathematics) | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 0 | 7 | |a Tensoranalysis |0 (DE-588)4204323-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mannigfaltigkeit |0 (DE-588)4037379-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Tensorrechnung |0 (DE-588)4192487-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematische Physik |0 (DE-588)4037952-8 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017371272 | ||
Datensatz im Suchindex
| _version_ | 1804138902247702528 |
|---|---|
| adam_text | CONTENTS
VECTOR
SPACES 1
1.1
Definitions, properties, and examples
1
1.2
Representation of vector spaces
5
1.3
Linear mappings
6
1.4
Representation of linear mappings
8
MULTILINEAR MAPPINGS AND DUAL SPACES
11
2.1
Vector spaces of linear mappings
11
2.2
Vector spaces of multilinear mappings
15
2.3
Nondegeuerate bilinear functions
19
2.4
Orthogonal
complementa
and the transpose of a linear mapping
20
TENSOR PRODUCT SPACES
25
3.1
The tensor product of two finite-dimensional vector spaces
25
3.2
Generalizations, isomorphisms, and a characterization
28
3.3
Tensor products of infinite-dimensional vector spaces
31
TENSORS
34
4.1
Definitions and alternative interpretations
34
4.2
The components of tensors
36
4.3
Mappings of the spaces VJ
39
SYMMETRIC AND SKEW-SYMMETRIC TENSORS
46
5.1
Symmetry and skew-symmetry
46
5.2
The symmetric subspace of Ks°
48
5.3
The skew-symmetric (alternating) subspace of V^
54
5.4
Some special properties of S2^*) and ^2(V*)
59
EXTERIOR
(GRASSMANN)
ALGEBRA
71
6.1
Tensor algebras
71
6.2
Definition and properties of the exterior product
72
6.3
Some more properties of the exterior product
77
THE TANGENT MAP OF REAL CARTESIAN SPACES
84
7.1
Maps of real cartesian spaces
84
7.2
The tangent and cotangent spaces at a point of Krl
88
7.3
The tangent map
96
TOPOLOGICAL SPACES
102
8.1
Definitions, properties, and examples
102
8.2
Continuous mappings
106
CONTENTS
9 DIFFERENTIABLE
MANIFOLDS
108
9.1
Definitions and examples
108
9.2
Mappings of differentiable manifolds
116
9.3
The tangent and cotangent spaces at a point of
M
119
9.4
Some properties of mappings
125
10
SUBMANIFOLDS
131
10.1
Parametrized submanifolds
131
10.2
Differentiable varieties as submanifolds
133
11
VECTOR FIELDS, 1-FORMS, AND OTHER
TENSOR FIELDS
136
11.1
Vector fields 136
11.2
1-Form fields
143
11.3
Tensor fields and differential forms
146
11.4
Mappings of tensor fields and differential forms
149
12
DIFFERENTIATION AND INTEGRATION OF
DIFFERENTIAL FORMS
153
12.1
Exterior differentiation of differential forms
153
12.2
Integration of differential forms
158
13
THE FLOW AND THE LIE DERIVATIVE OF A
VECTOR FIELD
168
13.1
Integral curves and the flow of a vector field
168
13.2
Flow boxes (local flows) and complete vector fields
172
13.3
Coordinate vector fields
176
13.4
The Lie derivative
178
14
INTEGRABILITY CONDITIONS FOR
DISTRIBUTIONS AND FOR PFAFFIAN SYSTEMS
186
14.1
Completely
integrable
distributions
186
14.2
Completely
integrable Pfaffian
systems
191
14.3
The characteristic distribution of a differential system
192
15
PSEUDO-RIEMANNIAN GEOMETRY
198
15.1
Pseudo-Rieniannian manifolds
198
15.2
Length and distance
204
15.3
Fiar
spaces
208
16
CONNECTION 1-FORMS
212
16.1
The Levi-Civita connection and its covariant derivative
212
lfi.2 Geodesies of the Levi-Civita connection
216
16.3 1
he torsion and curvature of a linear, or
affine
connection
21
J
16.4
The exponential map and normal coordinates
225
16.5
Connections on pseudo-Riemannian manifolds
226
CONTENTS
17
CONNECTIONS ON
MANIFOLDS
230
17.1
Connections
between
tangent
spaces
230
17.2
Coordinate-free description of a connection
231
17.3
The torsion and curvature of a connection
235
17.4
Some geometry of submanifolds
242
18
MECHANICS
248
18.1
Symplectic forms, symplectic mappings, Hamiltonian
vector fields, and
Poisson
brackets
248
18.2
The Darboux theorem, and the natural symplectic
structure of T*M
253
18.3
Hamilton s equations. Examples of mechanical systems
258
18.4
The Legendre transformation and Lagrangiaii vector fields
263
19
ADDITIONAL TOPICS IN MECHANICS
268
19.1
The configuration space as a pseudo-Riernannian manifold
208
19.2
The momentum mapping and Noether s theorem
271
19.3
Hamilton-Jacobi theory
275
20
A SPACETIME
282
20.1
Newton s mechanics and Maxwell s electromagnetic theory
282
20.2
Frames of reference generalized
287
20.3
The
Lorentz
transformations
289
20.4
Some properties and forms of the
Lorentz
transformations
294
20.5
Minkowski spacetime
298
21
SOME PHYSICS ON MINKOWSKI SPACETIME
306
21.1
Time dilation and the Lorentz-Fitzgerald contraction
306
21.2
Particle dynamics on Minkowski spacetime
313
21.3
Electromagnetism on Minkowski spacetime
317
21.4
Perfect fluids on Minkowski spacethne
322
22
EINSTEIN
SPACETIMES 326
22.1
Gravity, acceleration, and geodesies
326
22.2
Gravity is a manifestation of curvature
328
22.3
The field equation in empty space
331
22.4
Einstein s field equation
(Sitz, der Preuss
Acad.
Wissen., 1917) 334
23 SPACETIMES
NEAR AN ISOLATED STAR
339
23.1
Schwarzschilďs
exterior solution
330
23.2
Two applications of Schwar/.scliild s solution
344
23.3
The Kruskal extension of
Sehwarzschild
spacetime
348
23.4
The field of a rotating star
352
CONTENTS
24
NONEMPTY
SPACETIMES 356
24.1
Schwarzschild s interior solution
356
24.2
The form of the Friedmann-Robertson-Walker metric
tensor and its properties
361
24.3
Friedmann-Robertson-Walker spacetimes
365
25
LIE GROUPS
369
25.1
Definition and examples
369
25.2
Vector fields on a Lie group
371
25.3
Differential forms on a Lie group
377
25.4
The action of a Lie group on a manifold
380
26
FIBER BUNDLES
384
26.1
Principal fiber bundles
384
26.2
Examples
388
26.3
Associated bundles
390
26.4
Examples of associated bundles
392
27
CONNECTIONS ON FIBER BUNDLES
394
27.1
Connections on principal fiber bundles
394
27.2
Curvature
398
27.3
Linear Connections
401
27.4
Connections on vector bundles
404
28
GAUGE THEORY
409
28.1
Gauge transformation of a principal bundle
409
28.2
Gauge transformations of a vector bundle
413
28.3
How fiber bundles with connections form the basic
framework of the Standard Model of elementary particle
physics
417
References
423
Notation
427
Index
435
|
| any_adam_object | 1 |
| author | Wasserman, Robert H. 1926- |
| author_GND | (DE-588)1013629124 |
| author_facet | Wasserman, Robert H. 1926- |
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| author_variant | r h w rh rhw |
| building | Verbundindex |
| bvnumber | BV035451238 |
| classification_rvk | SK 370 SK 950 |
| classification_tum | PHY 013f MAT 535f MAT 530f |
| ctrlnum | (OCoLC)299242457 (DE-599)BVBBV035451238 |
| dewey-full | 530.15563 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15563 |
| dewey-search | 530.15563 |
| dewey-sort | 3530.15563 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| edition | 2. ed., 1. publ. in paperback |
| format | Book |
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| id | DE-604.BV035451238 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:35:34Z |
| institution | BVB |
| isbn | 9780199564828 9780198510598 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017371272 |
| oclc_num | 299242457 |
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| physical | XIV, 447 S. graph. Darst. |
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| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Wasserman, Robert H. 1926- Verfasser (DE-588)1013629124 aut Tensors and manifolds with applications to physics Robert H. Wasserman 2. ed., 1. publ. in paperback Oxford [u.a.] Oxford Univ. Press 2009 XIV, 447 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Mathematische Physik Calculus of tensors Manifolds (Mathematics) Mathematical physics Tensoranalysis (DE-588)4204323-2 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Tensorrechnung (DE-588)4192487-3 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Tensoranalysis (DE-588)4204323-2 s DE-604 Mannigfaltigkeit (DE-588)4037379-4 s Tensorrechnung (DE-588)4192487-3 s Mathematische Physik (DE-588)4037952-8 s Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017371272&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wasserman, Robert H. 1926- Tensors and manifolds with applications to physics Mathematische Physik Calculus of tensors Manifolds (Mathematics) Mathematical physics Tensoranalysis (DE-588)4204323-2 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Tensorrechnung (DE-588)4192487-3 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4204323-2 (DE-588)4037379-4 (DE-588)4192487-3 (DE-588)4037952-8 |
| title | Tensors and manifolds with applications to physics |
| title_auth | Tensors and manifolds with applications to physics |
| title_exact_search | Tensors and manifolds with applications to physics |
| title_full | Tensors and manifolds with applications to physics Robert H. Wasserman |
| title_fullStr | Tensors and manifolds with applications to physics Robert H. Wasserman |
| title_full_unstemmed | Tensors and manifolds with applications to physics Robert H. Wasserman |
| title_short | Tensors and manifolds |
| title_sort | tensors and manifolds with applications to physics |
| title_sub | with applications to physics |
| topic | Mathematische Physik Calculus of tensors Manifolds (Mathematics) Mathematical physics Tensoranalysis (DE-588)4204323-2 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Tensorrechnung (DE-588)4192487-3 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Mathematische Physik Calculus of tensors Manifolds (Mathematics) Mathematical physics Tensoranalysis Mannigfaltigkeit Tensorrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017371272&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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