Tensor calculus:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Alpha Science Internat.
2008
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 163 S. |
| ISBN: | 9781842654484 |
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Record in the Search Index
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| adam_text | TENSOR CALCULUS U.C.DE ABSOS ALI SHAIKH JOYDEEP SENGUPTA ALPHA SCIENCE
INTERNATIONAL LTD. HARROW U.K. CONTENTS PREFACE VII INTRODUCTION 1 I
SOME PRELIMINARIES 5 1.0 INTRODUCTION 5 1.1 SYSTEMS OF DIFFERENT ORDERS
5 1.2 SUMMATION CONVENTION . 6 1.3 KRONECKER SYMBOLS 7 1.4 SOME RESULTS
OF DETERMINANTS 8 1.5 DIFFERENTIATION OF A DETERMINANT 9 1.6 LINEAR
EQUATIONS, CRAMER S RULE 10 1.7 EXAMPLES 10 1.8 EXERCISES 13 II TENSOR
ALGEBRA 15 II.O INTRODUCTION 15 II. 1 N-DIMENSIONAL SPACE 15 11.2
TRANSFORMATION OF COORDINATES IN 5 N 16 11.3 INVARIANTS 17 11.4 VECTORS
18 11.4.1 COVARIANT VECTORS 18 11.4.2 CONTRAVARIANT VECTORS 19 11.5
TENSORS OF SECOND ORDER . 22 11.5.1 CONTRAVARIANT TENSORS OF ORDER TWO
22 11.5.2 COVARIANT TENSORS OF ORDER TWO 23 11.5.3 MIXED TENSORS OF
ORDER TWO 23 11.6 MIXED TENSORS OF TYPE (P, Q) 24 11.7 ZERO TENSOR 25
11.8 TENSOR FIELD 2 5 11.9 ALGEBRA OF TENSORS 25 11.10 EQUALITY OF TWO
TENSORS 27 11.11 SYMMETRIC AND SKEW-SYMMETRIC TENSORS 28 11.11. 1
SYMMETRIC TENSORS 28 11.11.2 SKEW-SYMMETRIC TENSORS 29 11.12 OUTER
MULTIPLICATION AND CONTRACTION 31 11.12.1 OUTER MULTIPLICATION 31
11.12.2 CONTRACTION 31 11.13 INNER MULTIPLICATION 33 11.14 QUOTIENT LAW
OF TENSORS 33 II. 14.1 QUOTIENT LAW FOR TENSORS OF FIRST ORDER AND TYPE
(0,1) . 33 II. 14.2 QUOTIENT LAW FOR TENSORS OF FIRST ORDER AND TYPE
(1,0) 34 II. 14.3 QUOTIENT LAW FOR COVARIANT TENSORS OF SECOND ORDER OR
OF TYPE (0,2) , . 34 II. 14.4 QUOTIENT LAW FOR CONTRAVARIANT TENSORS OF
SECOND ORDER OR OF TYPE (2,0) 35 II. 14.5 QUOTIENT LAW IN GENERAL FORM .
35 11.15 RECIPROCAL TENSOR OF A TENSOR 36 11.16 RELATIVE TENSOR 37 11.17
CROSS PRODUCT OR VECTOR PRODUCT OF TWO VECTORS 38 11.18 EXAMPLES 38
11.19 EXERCISES 61 III TENSOR CALCULUS 64 111.0 INTRODUCTION 64 111.1
RIEMANNIAN SPACE 66 III.L.L RIEMANNIAN METRIC 66 III. 1.2 RECIPROCAL OR
CONJUGATE TENSOR OF THE FUNDAMENTAL METRIC TENSOR GY 71 III. 1.3
ASSOCIATED TENSORS, LOWERING AND RAISING INDICES 74 III. 1.4 MAGNITUDE
OR LENGTH OF A VECTOR . . 78 III.1.5 UNIT VECTOR 79 III. 1.6 NULL VECTOR
. 79 111.1.7 ANGLE BETWEEN TWO NON-NULL VECTORS 80 111.1.8 ORTHOGONAL
VECTORS 81 111.2 CHRISTOFFEL SYMBOLS AND THEIR PROPERTIES 85 111.2.1
CHRISTOFFEL SYMBOLS OF FIRST KIND ,.-.. 85 111.2.2 CHRISTOFFEL SYMBOLS
OF SECOND KIND . 85 111.2.3 PROPERTIES OF CHRISTOFFEL SYMBOLS 86 111.2.4
LAW OF TRANSFORMATION OF CHRISTOFFEL SYMBOLS OF FIRST KIND 97 111.2.5
LAW OF TRANSFORMATION OF CHRISTOFFEL SYMBOLS OF SEC- OND KIND 99 111.3
COVARIANT DIFFERENTIATION OF TENSORS LOL 111.3.1 COVARIANT
DIFFERENTIATION OF A COVARIANT VECTOR . . . 102 111.3.2 COVARIANT
DIFFERENTIATION OF A CONTRAVARIANT VECTOR . 103 111.3.3 COVARIANT
DIFFERENTIATION OF TENSORS OF TYPE (0,2) . 104 111.3.4 COVARIANT
DERIVATIVE OF A TENSOR OF TYPE (2,0) ... 106 111.3.5 COVARIANT
DERIVATIVE OF A MIXED TENSOR OF TYPE (1,1) 107 111.3.6 COVARIANT
DERIVATIVE OF A MIXED TENSOR OF TYPE (P,Q) 111 111.3.7 RICCI S THEOREM :
112 111.3.8 GRADIENT OF A SCALAR 117 111.3.9 DIVERGENCE OF A
CONTRAVARIANT VECTOR . 117 XI III.3.10DIVERGENCE OF A COVARIANT VECTOR
118 III.3.1LCONSERVATIVE VECTOR . . 119 III.3.12DIVERGENCE OF A
CONTRAVARIANT TENSOR OF ORDER TWO 120 III.3.13DIVERGENCE OF A MIXED
TENSOR OF TYPE (1,1) 121 III.3.14LAPLACIAN OF AN INVARIANT 122
III.3.15CURL OF A COVARIANT VECTOR 123 111.4 RIEMANN-CHRISTOFFEL
CURVATURE TENSOR . 126 111.4.1 DEFINITION 126 111.4.2 PROPERTIES OF
RIEMANN-CHRISTOFFEL CURVATURE TENSOR 131 111.4.3 RICCI TENSOR 141
111.4.4 SCALAR CURVATURE 144 111.4.5 EINSTEIN SPACE 148 111.4.6 EINSTEIN
TENSOR 150 111.5 INTRINSIC DIFFERENTIATION 153 IV GEODESICS,RIEMANNIAN
COORDINATES AND GEODESIC COORDI- NATES 158 RV.L CALCULUS OF VARIATIONS
158 IV.2 FAMILIES OF CURVES 158 IV.3 EULER S CONDITIONS 159 IV.4
GEODESIES . 160 FV.5 RIEMANNIAN AND GEODESIC COORDINATES 162 V HISTORY
OF TENSOR CALCULUS 166 BIBLIOGRAPHY 168 INDEX 169
|
| adam_txt |
TENSOR CALCULUS U.C.DE ABSOS ALI SHAIKH JOYDEEP SENGUPTA ALPHA SCIENCE
INTERNATIONAL LTD. HARROW U.K. CONTENTS PREFACE VII INTRODUCTION 1 I
SOME PRELIMINARIES 5 1.0 INTRODUCTION 5 1.1 SYSTEMS OF DIFFERENT ORDERS
5 1.2 SUMMATION CONVENTION . 6 1.3 KRONECKER SYMBOLS 7 1.4 SOME RESULTS
OF DETERMINANTS 8 1.5 DIFFERENTIATION OF A DETERMINANT 9 1.6 LINEAR
EQUATIONS, CRAMER'S RULE 10 1.7 EXAMPLES 10 1.8 EXERCISES 13 II TENSOR
ALGEBRA 15 II.O INTRODUCTION 15 II. 1 N-DIMENSIONAL SPACE 15 11.2
TRANSFORMATION OF COORDINATES IN 5 N 16 11.3 INVARIANTS 17 11.4 VECTORS
18 11.4.1 COVARIANT VECTORS 18 11.4.2 CONTRAVARIANT VECTORS 19 11.5
TENSORS OF SECOND ORDER . 22 11.5.1 CONTRAVARIANT TENSORS OF ORDER TWO
22 11.5.2 COVARIANT TENSORS OF ORDER TWO 23 11.5.3 MIXED TENSORS OF
ORDER TWO 23 11.6 MIXED TENSORS OF TYPE (P, Q) 24 11.7 ZERO TENSOR 25
11.8 TENSOR FIELD 2 5 11.9 ALGEBRA OF TENSORS 25 11.10 EQUALITY OF TWO
TENSORS 27 11.11 SYMMETRIC AND SKEW-SYMMETRIC TENSORS 28 11.11. 1
SYMMETRIC TENSORS 28 11.11.2 SKEW-SYMMETRIC TENSORS 29 11.12 OUTER
MULTIPLICATION AND CONTRACTION 31 11.12.1 OUTER MULTIPLICATION 31
11.12.2 CONTRACTION 31 11.13 INNER MULTIPLICATION 33 11.14 QUOTIENT LAW
OF TENSORS 33 II. 14.1 QUOTIENT LAW FOR TENSORS OF FIRST ORDER AND TYPE
(0,1) . 33 II. 14.2 QUOTIENT LAW FOR TENSORS OF FIRST ORDER AND TYPE
(1,0) 34 II. 14.3 QUOTIENT LAW FOR COVARIANT TENSORS OF SECOND ORDER OR
OF TYPE (0,2) , . 34 II. 14.4 QUOTIENT LAW FOR CONTRAVARIANT TENSORS OF
SECOND ORDER OR OF TYPE (2,0) 35 II. 14.5 QUOTIENT LAW IN GENERAL FORM .
35 11.15 RECIPROCAL TENSOR OF A TENSOR 36 11.16 RELATIVE TENSOR 37 11.17
CROSS PRODUCT OR VECTOR PRODUCT OF TWO VECTORS 38 11.18 EXAMPLES 38
11.19 EXERCISES 61 III TENSOR CALCULUS 64 111.0 INTRODUCTION 64 111.1
RIEMANNIAN SPACE 66 III.L.L RIEMANNIAN METRIC 66 III. 1.2 RECIPROCAL OR
CONJUGATE TENSOR OF THE FUNDAMENTAL METRIC TENSOR GY 71 III. 1.3
ASSOCIATED TENSORS, LOWERING AND RAISING INDICES 74 III. 1.4 MAGNITUDE
OR LENGTH OF A VECTOR . . 78 III.1.5 UNIT VECTOR 79 III. 1.6 NULL VECTOR
. 79 111.1.7 ANGLE BETWEEN TWO NON-NULL VECTORS 80 111.1.8 ORTHOGONAL
VECTORS 81 111.2 CHRISTOFFEL SYMBOLS AND THEIR PROPERTIES 85 111.2.1
CHRISTOFFEL SYMBOLS OF FIRST KIND ',.-. 85 111.2.2 CHRISTOFFEL SYMBOLS
OF SECOND KIND . 85 111.2.3 PROPERTIES OF CHRISTOFFEL SYMBOLS 86 111.2.4
LAW OF TRANSFORMATION OF CHRISTOFFEL SYMBOLS OF FIRST KIND 97 111.2.5
LAW OF TRANSFORMATION OF CHRISTOFFEL SYMBOLS OF SEC- OND KIND 99 111.3
COVARIANT DIFFERENTIATION OF TENSORS LOL 111.3.1 COVARIANT
DIFFERENTIATION OF A COVARIANT VECTOR . . . 102 111.3.2 COVARIANT
DIFFERENTIATION OF A CONTRAVARIANT VECTOR . 103 111.3.3 COVARIANT
DIFFERENTIATION OF TENSORS OF TYPE (0,2) . 104 111.3.4 COVARIANT
DERIVATIVE OF A TENSOR OF TYPE (2,0) . 106 111.3.5 COVARIANT
DERIVATIVE OF A MIXED TENSOR OF TYPE (1,1) 107 111.3.6 COVARIANT
DERIVATIVE OF A MIXED TENSOR OF TYPE (P,Q) 111 111.3.7 RICCI'S THEOREM :
112 111.3.8 GRADIENT OF A SCALAR 117 111.3.9 DIVERGENCE OF A
CONTRAVARIANT VECTOR . 117 XI III.3.10DIVERGENCE OF A COVARIANT VECTOR
118 III.3.1LCONSERVATIVE VECTOR . . 119 III.3.12DIVERGENCE OF A
CONTRAVARIANT TENSOR OF ORDER TWO 120 III.3.13DIVERGENCE OF A MIXED
TENSOR OF TYPE (1,1) 121 III.3.14LAPLACIAN OF AN INVARIANT 122
III.3.15CURL OF A COVARIANT VECTOR 123 111.4 RIEMANN-CHRISTOFFEL
CURVATURE TENSOR . 126 111.4.1 DEFINITION 126 111.4.2 PROPERTIES OF
RIEMANN-CHRISTOFFEL CURVATURE TENSOR 131 111.4.3 RICCI TENSOR 141
111.4.4 SCALAR CURVATURE 144 111.4.5 EINSTEIN SPACE 148 111.4.6 EINSTEIN
TENSOR 150 111.5 INTRINSIC DIFFERENTIATION 153 IV GEODESICS,RIEMANNIAN
COORDINATES AND GEODESIC COORDI- NATES 158 RV.L CALCULUS OF VARIATIONS
158 IV.2 FAMILIES OF CURVES 158 IV.3 EULER'S CONDITIONS 159 IV.4
GEODESIES . 160 FV.5 RIEMANNIAN AND GEODESIC COORDINATES 162 V HISTORY
OF TENSOR CALCULUS 166 BIBLIOGRAPHY 168 INDEX 169 |
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| id | DE-604.BV035115417 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T22:19:22Z |
| indexdate | 2024-07-09T21:22:39Z |
| institution | BVB |
| isbn | 9781842654484 |
| language | English |
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| physical | XI, 163 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
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| publisher | Alpha Science Internat. |
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| spelling | De, Uday Chand Verfasser (DE-588)136704794 aut Tensor calculus U. C. De ; Absos Ali Shaikh ; Joydeep Sengupta 2. ed. Oxford Alpha Science Internat. 2008 XI, 163 S. txt rdacontent n rdamedia nc rdacarrier Calculus of tensors Calcul tensoriel Tensoralgebra (DE-588)4505278-5 gnd rswk-swf Tensorrechnung (DE-588)4192487-3 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Tensoralgebra (DE-588)4505278-5 s Tensorrechnung (DE-588)4192487-3 s Differentialgeometrie (DE-588)4012248-7 s DE-604 Shaikh, Absos Ali Sonstige (DE-588)136704840 oth Sengupta, Joydeep Sonstige oth GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016783172&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | De, Uday Chand Tensor calculus Calculus of tensors Calcul tensoriel Tensoralgebra (DE-588)4505278-5 gnd Tensorrechnung (DE-588)4192487-3 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4505278-5 (DE-588)4192487-3 (DE-588)4012248-7 |
| title | Tensor calculus |
| title_auth | Tensor calculus |
| title_exact_search | Tensor calculus |
| title_exact_search_txtP | Tensor calculus |
| title_full | Tensor calculus U. C. De ; Absos Ali Shaikh ; Joydeep Sengupta |
| title_fullStr | Tensor calculus U. C. De ; Absos Ali Shaikh ; Joydeep Sengupta |
| title_full_unstemmed | Tensor calculus U. C. De ; Absos Ali Shaikh ; Joydeep Sengupta |
| title_short | Tensor calculus |
| title_sort | tensor calculus |
| topic | Calculus of tensors Calcul tensoriel Tensoralgebra (DE-588)4505278-5 gnd Tensorrechnung (DE-588)4192487-3 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Calculus of tensors Calcul tensoriel Tensoralgebra Tensorrechnung Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016783172&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT deudaychand tensorcalculus AT shaikhabsosali tensorcalculus AT senguptajoydeep tensorcalculus |