Vector analysis and Cartesian tensors
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| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
New York
Jovanovich
1977
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Bourne, Donald E. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Vector analysis and Cartesian tensors |c Donald E. Bourne ; Peter C. Kendall* |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York |b Jovanovich |c 1977 | |
| 300 | |a IX, 256 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0834 MA.86 |
|---|---|
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| DE-BY-TUM_location | LSB |
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| _version_ | 1820853677090406400 |
| adam_text | CONTENTS
Preface
Chapter 1 Rectangular Cartesian Coordinates and Rotation
of Axes
1.1 Rectangular cartesian coordinates 1
1.2 Direction cosines and direction ratios 5
1.3 Angles between lines through the origin 6
1.4 The orthogonal projection of one line on another 7
1.5 Rotation of axes 9
1.6 The summation convention and its use 13
1.7 Invariance with respect to a rotation of the axes 16
1.8 Matrix notation 17
Chapter 2 Scalar and Vector Algebra
2.1 Scalars 18
2.2 Vectors: basic notions 19
2.3 Multiplication of a vector by a scalar 24
2.4 Addition and subtraction of vectors 27
2.5 The unit vectors i, j, k 31
2.6 Scalar products 31
2.7 Vector products 36
2.8 The triple scalar product 43
2.9 The triple vector product 46
2.10 Products of four vectors 47
2.11 Bound vectors 47
Chapter 3 Vector Functions of a Real Variable. Differential
Geometry of Curves
3.1 Vector functions and their geometrical representation 49
3.2 Differentiation of vectors 53
3.3 Differentiation rules 55
3.4 The tangent to a curve. Smooth, piecewise smooth, and
simple curves 56
3.5 Arc length 61
3.6 Curvature and torsion 63
3.7 Applications in kinematics 67
viii CONTENTS
Chapter 4 Scalar and Vector Fields
4.1 Regions 72
4.2 Functions of several variables 73
4.3 Definitions of scalar and vector fields 78
4.4 Gradient of a scalar field 78
4.5 Properties of gradient 81
4.6 The divergence and curl of a vector field 85
4.7 The del operator 87
4.8 Scalar invariant operators 91
4.9 Useful identities 94
4.10 Cylindrical and spherical polar coordinates 98
4.11 General orthogonal curvilinear coordinates 102
4.12 Vector components in orthogonal curvilinear coordinates 107
4.13 Expressions for grad Q, div F, curl F, and V2 in orthogonal
curvilinear coordinates 109
4.14 Vector analysis in w dimensional space 115
Chapter 5 Line, Surface, and Volume Integrals
5.1 Line integral of a scalar field 116
5.2 Line integrals of a vector field 121
5.3 Repeated integrals 123
5.4 Double and triple integrals 125
5.5 Surfaces 138
5.6 Surface integrals 147
5.7 Volume integrals 154
Chapter 6 Integral Theorems
6.1 Introduction 159
6.2 The Divergence Theorem (Gauss s theorem) 159
6.3 Green s theorems 168
6.4 Stokes s theorem 172
6.5 Limit definitions of div F and curl F 182
6.6 Geometrical and physical significance of divergence and
curl 183
Chapter 7 Applications in Potential Theory
7.1 Connectivity 186
7.2 The scalar potential 187
7.3 The vector potential 190
7.4 Poisson s equation 193
CONTENTS ix
7.5 Poisson s equation in vector form 198
7.6 Helmholtz s theorem 198
7.7 Solid angles 199
Chapter 8 Cartesian Tensors
8.1 Introduction 204
8.2 Cartesian tensors: basic algebra 205
8.3 Isotropic tensors 210
8.4 Tensor fields 218
8.5 The divergence theorem in tensor field theory 222
Chapter 9 Representation Theorems for Isotropic Tensor
Functions
9.1 Introduction 224
9.2 Diagonalization of second order symmetrical tensors 225
9.3 Invariants of second order symmetrical tensors 229
9.4 Representation of isotropic vector functions 231
9.5 Isotropic scalar functions of symmetrical second order
tensors 233
9.6 Representation of an isotropic tensor function 235
Appendix 1 Determinants 239
Appendix 2 The chain rule for Jacobians 241
Appendix 3 Expressions for grad, div, curl, and V2 in cylindri¬
cal and spherical polar coordinates 242
Answers to Exercises 243
Index 251
|
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| author | Bourne, Donald E. Kendall, Peter C. 1934- |
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| discipline | Mathematik |
| edition | 2. ed. |
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| id | DE-604.BV002253032 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T10:33:15Z |
| institution | BVB |
| isbn | 0121190501 |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001480486 |
| oclc_num | 251501865 |
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| owner | DE-91 DE-BY-TUM DE-355 DE-BY-UBR DE-29T DE-188 |
| owner_facet | DE-91 DE-BY-TUM DE-355 DE-BY-UBR DE-29T DE-188 |
| physical | IX, 256 S. graph. Darst. |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
| publisher | Jovanovich |
| record_format | marc |
| spellingShingle | Bourne, Donald E. Kendall, Peter C. 1934- Vector analysis and Cartesian tensors Tensoranalysis (DE-588)4204323-2 gnd Vektoranalysis (DE-588)4191992-0 gnd |
| subject_GND | (DE-588)4204323-2 (DE-588)4191992-0 |
| title | Vector analysis and Cartesian tensors |
| title_auth | Vector analysis and Cartesian tensors |
| title_exact_search | Vector analysis and Cartesian tensors |
| title_full | Vector analysis and Cartesian tensors Donald E. Bourne ; Peter C. Kendall* |
| title_fullStr | Vector analysis and Cartesian tensors Donald E. Bourne ; Peter C. Kendall* |
| title_full_unstemmed | Vector analysis and Cartesian tensors Donald E. Bourne ; Peter C. Kendall* |
| title_short | Vector analysis and Cartesian tensors |
| title_sort | vector analysis and cartesian tensors |
| topic | Tensoranalysis (DE-588)4204323-2 gnd Vektoranalysis (DE-588)4191992-0 gnd |
| topic_facet | Tensoranalysis Vektoranalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001480486&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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