Vector calculus:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
London [u.a.]
Springer
1998
|
| Ausgabe: | 2. print., with corr. |
| Schriftenreihe: | Springer undergraduate mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 182 S. graph. Darst. |
| ISBN: | 3540761802 |
Internformat
MARC
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| 100 | 1 | |a Matthews, Paul Charles |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Vector calculus |c P. C. Matthews |
| 250 | |a 2. print., with corr. | ||
| 264 | 1 | |a London [u.a.] |b Springer |c 1998 | |
| 300 | |a IX, 182 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804127421313581056 |
|---|---|
| adam_text | IMAGE 1
TABLE OF CONTENTS
1. VECTOR ALGEBRA 1
1.1 VECTORS AND SCALARS 1
1.1.1 DEFINITION OF A VECTOR AND A SCALAR 1
1.1.2 ADDITION OF VECTORS 2
1.1.3 COMPONENTS OF A VECTOR 3
1.2 DOT PRODUCT 4
1.2.1 APPLICATIONS OF THE DOT PRODUCT 7
1.3 CROSS PRODUCT 9
1.3.1 APPLICATIONS OF THE CROSS PRODUCT 11
1.4 SCALAR TRIPLE PRODUCT 14
1.5 VECTOR TRIPLE PRODUCT 16
1.6 SCALAR FIELDS AND VECTOR FIELDS 17
2. LINE, SURFACE AND VOLUME INTEGRALS 21
2.1 APPLICATIONS AND METHODS OF INTEGRATION 21
2.1.1 EXAMPLES OF THE USE OF INTEGRATION 21
2.1.2 INTEGRATION BY SUBSTITUTION 22
2.1.3 INTEGRATION BY PARTS 23
2.2 LINE INTEGRALS 25
2.2.1 INTRODUCTORY EXAMPLE: WORK DONE AGAINST A FORCE 25 2.2.2
EVALUATION OF LINE INTEGRALS 26
2.2.3 CONSERVATIVE VECTOR FIELDS 28
2.2.4 OTHER FORMS OF LINE INTEGRALS 30
2.3 SURFACE INTEGRALS 31
2.3.1 INTRODUCTORY EXAMPLE: FLOW THROUGH A PIPE 31
2.3.2 EVALUATION OF SURFACE INTEGRALS 33
2.3.3 OTHER FORMS OF SURFACE INTEGRALS 38
2.4 VOLUME INTEGRALS 39
IMAGE 2
VECTOR CALCULUS
2.4.1 INTRODUCTORY EXAMPLE: MASS OF AN OBJECT WITH VARIABLE
DENSITY 39
2.4.2 EVALUATION OF VOLUME INTEGRALS 40
3. GRADIENT, DIVERGENCE AND CURL 45
3.1 PARTIAL DIFFERENTIATION AND TAYLOR SERIES 45
3.1.1 PARTIAL DIFFERENTIATION 45
3.1.2 TAYLOR SERIES IN MORE THAN ONE VARIABLE 47
3.2 GRADIENT OF A SCALAR FIELD 48
3.2.1 GRADIENTS, CONSERVATIVE FIELDS AND POTENTIALS 51 3.2.2 PHYSICAL
APPLICATIONS OF THE GRADIENT 52
3.3 DIVERGENCE OF A VECTOR FIELD 53
3.3.1 PHYSICAL INTERPRETATION OF DIVERGENCE 56
3.3.2 LAPLACIAN OF A SCALAR FIELD 56
3.4 CURL OF A VECTOR FIELD 58
3.4.1 PHYSICAL INTERPRETATION OF CURL 60
3.4.2 RELATION BETWEEN CURL AND ROTATION 61
3.4.3 CURL AND CONSERVATIVE VECTOR FIELDS 61
4. SUFFIX NOTATION AND ITS APPLICATIONS 65
4.1 INTRODUCTION TO SUFFIX NOTATION 65
4.2 THE KRONECKER DELTA $*,* 68
4.3 THE ALTERNATING TENSOR E^FC 70
4.4 RELATION BETWEEN EIJK AND SIJ 72
4.5 GRAD, DIV AND CURL IN SUFFIX NOTATION 74
4.6 COMBINATIONS OF GRAD, DIV AND CURL 76
4.7 GRAD, DIV AND CURL APPLIED TO PRODUCTS OF FUNCTIONS 78
5. INTEGRAL THEOREMS 83
5.1 DIVERGENCE THEOREM 83
5.1.1 CONSERVATION OF MASS FOR A FLUID 85
5.1.2 APPLICATIONS OF THE DIVERGENCE THEOREM 87
5.1.3 RELATED THEOREMS LINKING SURFACE AND VOLUME INTEGRALS .. 88 5.2
STOKES S THEOREM 91
5.2.1 APPLICATIONS OF STOKES S THEOREM 93
5.2.2 RELATED THEOREMS LINKING LINE AND SURFACE INTEGRALS 95
6. CURVILINEAR COORDINATES 99
6.1 ORTHOGONAL CURVILINEAR COORDINATES 99
6.2 GRAD, DIV AND CURL IN ORTHOGONAL CURVILINEAR COORDINATE SYSTEMS 104
6.2.1 GRADIENT 104
6.2.2 DIVERGENCE 105
IMAGE 3
TABIE OF CONTENTS IX
6.2.3 CURL 106
6.3 CYLINDRICAL POLAR COORDINATES 107
. 6.4 SPHERICAL POLAR COORDINATES 110
7. CARTESIAN TENSORS 115
7.1 COORDINATE TRANSFORMATIONS 115
7.2 VECTORS AND SCALARS 117
7.3 TENSORS 119
7.3.1 THE QUOTIENT RULE 120
7.3.2 SYMMETRIC AND ANTI-SYMMETRIC TENSORS 122
7.3.3 ISOTROPIC TENSORS 123
7.4 PHYSICAL EXAMPLES OF TENSORS 126
7.4.1 OHM S LAW 126
7.4.2 THE INERTIA TENSOR 127
8. APPLICATIONS OF VECTOR CALCULUS 131
8.1 HEAT TRANSFER 132
8.2 ELECTROMAGNETISM 134
8.2.1 ELECTROSTATICS 135
8.2.2 ELECTROMAGNETIC WAVES IN A VACUUM 137
8.3 CONTINUUM MECHANICS AND THE STRESS TENSOR 140
8.4 SOLID MECHANICS 143
8.5 FLUID MECHANICS 145
8.5.1 EQUATION OF MOTION FOR A FLUID 146
8.5.2 THE VORTICITY EQUATION 147
8.5.3 BERNOULLI S EQUATION 149
SOLUTIONS 153
INDEX 181
|
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| ctrlnum | (OCoLC)41626834 (DE-599)BVBBV012754823 |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| edition | 2. print., with corr. |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV012754823 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:33:05Z |
| institution | BVB |
| isbn | 3540761802 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008672413 |
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| physical | IX, 182 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer undergraduate mathematics series |
| spelling | Matthews, Paul Charles Verfasser aut Vector calculus P. C. Matthews 2. print., with corr. London [u.a.] Springer 1998 IX, 182 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer undergraduate mathematics series Vector analysis Vektorrechnung (DE-588)4062471-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Vektorrechnung (DE-588)4062471-7 s DE-604 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008672413&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Matthews, Paul Charles Vector calculus Vector analysis Vektorrechnung (DE-588)4062471-7 gnd |
| subject_GND | (DE-588)4062471-7 (DE-588)4123623-3 |
| title | Vector calculus |
| title_auth | Vector calculus |
| title_exact_search | Vector calculus |
| title_full | Vector calculus P. C. Matthews |
| title_fullStr | Vector calculus P. C. Matthews |
| title_full_unstemmed | Vector calculus P. C. Matthews |
| title_short | Vector calculus |
| title_sort | vector calculus |
| topic | Vector analysis Vektorrechnung (DE-588)4062471-7 gnd |
| topic_facet | Vector analysis Vektorrechnung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008672413&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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