Tensor calculus, relativity, and cosmology: a first course
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier Academic Press
2005
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 280 S. graph. Darst. |
| ISBN: | 012200681X 9780122006814 |
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Record in the Search Index
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| adam_text | TENSOR CALCULUS, RELATIVITY, AND COSMOLOGY A FIRST COURSE BY M.
DALARSSON ERICSSON RESEARCH AND DEVELOPMENT STOCKHOLM, SWEDEN AND N.
DALARSSON ROYAL INSTITUTE OF TECHNOLOGY STOCKHOLM, SWEDEN ELSEVIER
ACADEMIC PRESS AMSTERDAM * BOSTON * HEIDELBERG * LONDON * NEW YORK *
OXFORD PARIS * SAN DIEGO * SAN FRANCISCO * SINGAPORE * SYDNEY * TOKYO
CONTENTS 1 INTRODUCTION 1 PART I TENSOR ALGEBRA 3 2 NOTATION AND SYSTEMS
OF NUMBERS 5 2.1 INTRODUCTION AND BASIC CONCEPTS 5 2.2 SYMMETRIC AND
ANTISYMMETRIC SYSTEMS 7 2.3 OPERATIONS WITH SYSTEMS 8 2.3.1 ADDITION AND
SUBTRACTION OF SYSTEMS 8 2.3.2 DIRECT PRODUCT OF SYSTEMS 8 2.3.3
CONTRACTION OF SYSTEMS 9 2.3.4 COMPOSITION OF SYSTEMS 9 2.4 SUMMATION
CONVENTION 10 2.5 UNIT SYMMETRIC AND ANTISYMMETRIC SYSTEMS 11 3 VECTOR
SPACES 15 3.1 INTRODUCTION AND BASIC CONCEPTS 15 3.2 DEFINITION OF A
VECTOR SPACE 16 3.3 THE EUCLIDEAN METRIC SPACE 18 3.4 THE RIEMANNIAN
SPACES 18 4 DEFINITIONS OF TENSORS 23 4.1 TRANSFORMATIONS OF VARIABLES
23 4.2 CONTRAVARIANT VECTORS 24 4.3 COVARIANT VECTORS 24 4.4 INVARIANTS
(SCALARS) 24 4.5 CONTRAVARIANT TENSORS 25 4.6 COVARIANT TENSORS 26 VII
VIII CONTENTS 4.7 MIXED TENSORS 26 4.8 SYMMETRY PROPERTIES OF TENSORS 27
4.9 SYMMETRIC AND ANTISYMMETRIC PARTS OF TENSORS 28 4.10 TENSOR
CHARACTER OF SYSTEMS 30 5 RELATIVE TENSORS 33 5.1 INTRODUCTION AND
DEFINITIONS 33 5.2 UNIT ANTISYMMETRIC TENSORS 34 5.3 VECTOR PRODUCT IN
THREE DIMENSIONS 36 5.4 MIXED PRODUCT IN THREE DIMENSIONS 38 5.5
ORTHOGONAL COORDINATE TRANSFORMATIONS 39 5.5.1 ROTATIONS OF DESCARTES
COORDINATES 39 5.5.2 TRANSLATIONS OF DESCARTES COORDINATES 41 5.5.3
INVERSIONS OF DESCARTES COORDINATES 41 5.5.4 AXIAL VECTORS AND
PSEUDOSCALARS IN DESCARTES COORDINATES 42 6 THE METRIC TENSOR 43 6.1
INTRODUCTION AND DEFINITIONS 43 6.2 ASSOCIATED VECTORS AND TENSORS 46
6.3 ARC LENGTH OF CURVES: UNIT VECTORS 48 6.4 ANGLES BETWEEN VECTORS 49
6.5 SCHWARZ INEQUALITY 51 6.6 ORTHOGONAL AND PHYSICAL VECTOR COORDINATES
52 7 TENSORS AS LINEAR OPERATORS 55 PART II TENSOR ANALYSIS 59 8 TENSOR
DERIVATIVES 61 8.1 DIFFERENTIALS OF TENSORS 61 8.1.1 DIFFERENTIALS OF
CONTRAVARIANT VECTORS 64 8.1.2 DIFFERENTIALS OF COVARIANT VECTORS 64 8.2
COVARIANT DERIVATIVES 65 8.2.1 COVARIANT DERIVATIVES OF VECTORS 65 8.2.2
COVARIANT DERIVATIVES OF TENSORS 66 8.3 PROPERTIES OF COVARIANT
DERIVATIVES 67 8.4 ABSOLUTE DERIVATIVES OF TENSORS 69 9 CHRISTOFFEL
SYMBOLS 71 9.1 PROPERTIES OF CHRISTOFFEL SYMBOLS 71 9.2 RELATION TO THE
METRIC TENSOR 74 CONTENTS IX 10 DIFFERENTIAL OPERATORS 79 10.1 THE
HAMILTONIAN V-OPERATOR 79 10.2 GRADIENT OF SCALARS 79 10.3 DIVERGENCE OF
VECTORS AND TENSORS 80 10.4 CURL OF VECTORS 82 10.5 LAPLACIAN OF SCALARS
AND TENSORS 83 10.6 INTEGRAL THEOREMS FOR TENSOR FIELDS 85 10.6.1 STOKES
THEOREM 85 10.6.2 GAUSS THEOREM 86 11 GEODESIC LINES 89 11.1 LAGRANGE
EQUATIONS 89 11.2 GEODESIC EQUATIONS 92 12 THE CURVATURE TENSOR 97 12.1
DEFINITION OF THE CURVATURE TENSOR 97 12.2 PROPERTIES OF THE CURVATURE
TENSOR 100 12.3 COMMUTATOR OF COVARIANT DERIVATIVES 103 12.4 RICCI
TENSOR AND SCALAR 104 12.5 CURVATURE TENSOR COMPONENTS 105 PART III
SPECIAL THEORY OF RELATIVITY 109 13 RELATIVISTIC KINEMATICS 111 13.1 THE
PRINCIPLE OF RELATIVITY 111 13.2 INVARIANCE OF THE SPEED OF LIGHT 112
13.3 THE INTERVAL BETWEEN EVENTS 112 13.4 LORENTZ TRANSFORMATIONS 116
13.5 VELOCITY AND ACCELERATION VECTORS 119 14 RELATIVISTIC DYNAMICS 123
14.1 LAGRANGE EQUATIONS 123 14.2 ENERGY-MOMENTUM VECTOR 125 14.2.1
INTRODUCTION AND DEFINITIONS 125 14.2.2 TRANSFORMATIONS OF
ENERGY-MOMENTUM 128 14.2.3 CONSERVATION OF ENERGY-MOMENTUM 130 14.3
ANGULAR MOMENTUM TENSOR 131 15 ELECTROMAGNETIC FIELDS 135 15.1
ELECTROMAGNETIC FIELD TENSOR 135 15.2 GAUGE INVARIANCE 140 15.3 LORENTZ
TRANSFORMATIONS AND INVARIANTS 142 X CONTENTS 16 ELECTROMAGNETIC FIELD
EQUATIONS 147 16.1 ELECTROMAGNETIC CURRENT VECTOR 147 16.2
MAXWELLEQUATIONS 149 16.3 ELECTROMAGNETIC POTENTIALS 154 16.4
ENERGY-MOMENTUM TENSOR 155 PART IV GENERAL THEORY OF RELATIVITY 163 17
GRAVITATIONAL FIELDS 165 17.1 INTRODUCTION 165 17.2 TIME INTERVALS AND
DISTANCES 167 17.3 PARTICLE DYNAMICS 169 17.4 ELECTROMAGNETIC FIELD
EQUATIONS 173 18 GRAVITATIONAL FIELD EQUATIONS 177 18.1 THE ACTION
INTEGRAL 177 18.2 ACTION FOR MATTER FIELDS 182 18.3 EINSTEIN FIELD
EQUATIONS 188 19 SOLUTIONS OF FIELD EQUATIONS 193 19.1 THE NEWTON LAW
193 19.2 THE SCHWARZSCHILD SOLUTION 195 20 APPLICATIONS OF THE
SCHWARZSCHILD METRIC 207 20.1 THE PERIHELION ADVANCE 207 20.2 BLACK
HOLES 215 PART V ELEMENTS OF COSMOLOGY 223 21 THE ROBERTSON-WALKER
METRIC 225 21.1 INTRODUCTION AND BASIC OBSERVATIONS 225 21.2 METRIC
DEFINITION AND PROPERTIES 227 21.3 THE HUBBLE LAW 234 21.4 THE
COSMOLOGICAL RED SHIFTS 235 22 COSMIC DYNAMICS 239 22.1 THE EINSTEIN
TENSOR 239 22.2 THE FRIEDMANN EQUATIONS 250 23 NONSTATIC MODELS OF THE
UNIVERSE 253 23.1 SOLUTIONS OF THE FRIEDMANN EQUATIONS 253 23.1.1 THE
FLAT MODEL (K = 0) 255 CONTENTS XI 23.1.2 THE CLOSED MODEL (K = 1) 255
23.1.3 THE OPEN MODEL (K = -1) 257 23.2 CLOSED OR OPEN UNIVERSE 258 23.3
NEWTONIAN COSMOLOGY 260 24 QUANTUM COSMOLOGY 265 24.1 INTRODUCTION 265
24.2 THE WHEELER-DEWITT EQUATION 266 24.3 THE WAVE FUNCTION OF THE
UNIVERSE 270 BIBLIOGRAHY 275 INDEX 277
|
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| dewey-ones | 512 - Algebra |
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| dewey-sort | 3512.57 |
| dewey-tens | 510 - Mathematics |
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| isbn | 012200681X 9780122006814 |
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| spelling | Dalarsson, Mirjana Verfasser aut Tensor calculus, relativity, and cosmology a first course by M. Dalarsson and N. Dalarsson Tensors, relativity, and cosmology Amsterdam [u.a.] Elsevier Academic Press 2005 XI, 280 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Relativitätstheorie (DE-588)4049363-5 gnd rswk-swf Kosmologie (DE-588)4114294-9 gnd rswk-swf Tensoranalysis (DE-588)4204323-2 gnd rswk-swf Tensoranalysis (DE-588)4204323-2 s DE-604 Relativitätstheorie (DE-588)4049363-5 s Kosmologie (DE-588)4114294-9 s Dalarsson, Nils Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020163869&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dalarsson, Mirjana Dalarsson, Nils Tensor calculus, relativity, and cosmology a first course Relativitätstheorie (DE-588)4049363-5 gnd Kosmologie (DE-588)4114294-9 gnd Tensoranalysis (DE-588)4204323-2 gnd |
| subject_GND | (DE-588)4049363-5 (DE-588)4114294-9 (DE-588)4204323-2 |
| title | Tensor calculus, relativity, and cosmology a first course |
| title_alt | Tensors, relativity, and cosmology |
| title_auth | Tensor calculus, relativity, and cosmology a first course |
| title_exact_search | Tensor calculus, relativity, and cosmology a first course |
| title_full | Tensor calculus, relativity, and cosmology a first course by M. Dalarsson and N. Dalarsson |
| title_fullStr | Tensor calculus, relativity, and cosmology a first course by M. Dalarsson and N. Dalarsson |
| title_full_unstemmed | Tensor calculus, relativity, and cosmology a first course by M. Dalarsson and N. Dalarsson |
| title_short | Tensor calculus, relativity, and cosmology |
| title_sort | tensor calculus relativity and cosmology a first course |
| title_sub | a first course |
| topic | Relativitätstheorie (DE-588)4049363-5 gnd Kosmologie (DE-588)4114294-9 gnd Tensoranalysis (DE-588)4204323-2 gnd |
| topic_facet | Relativitätstheorie Kosmologie Tensoranalysis |
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