A brief on tensor analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Springer
1994
|
| Edition: | 2. ed. |
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 112 S. graph. Darst. |
| ISBN: | 9780387940885 038794088X 354094088X |
Staff View
MARC
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| 100 | 1 | |a Simmonds, James G. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A brief on tensor analysis |c James G. Simmonds |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York u.a. |b Springer |c 1994 | |
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Record in the Search Index
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| adam_text | Contents
Preface to the Second Edition vii
Preface to the First Edition ix
CHAPTER I
Introduction: Vectors and Tensors 1
Three Dimensional Euclidean Space 3
Directed Line Segments 3
Addition of Two Vectors 4
Multiplication of a Vector v by a Scalar a 5
Things That Vectors May Represent 5
Cartesian Coordinates 6
The Dot Product 7
Cartesian Base Vectors 10
The Interpretation of Vector Addition 10
The Cross Product 11
Alternative Interpretation of the Dot and Cross Product. Tensors 15
Definitions 16
The Cartesian Components of a Second Order Tensor 17
The Cartesian Basis for Second Order Tensors 19
Exercises 20
CHAPTER II
General Bases and Tensor Notation 25
General Bases 25
The Jacobian of a Basis Is Nonzero 27
The Summation Convention 27
xiii
xiv Contents
Computing the Dot Product in a General Basis 28
Reciprocal Base Vectors 28
The Roof (Contravariant) and Cellar (Covariant) Components
of a Vector 30
Simplification of the Component Form of the Dot Product in a
General Basis 31
Computing the Cross Product in a General Basis 32
A Second Order Tensor Has Four Sets of Components in General 34
Change of Basis 36
Exercises 38
CHAPTER III
Newton s Law and Tensor Calculus 45
Rigid Bodies 45
New Conservation Laws 46
Nomenclature 47
Newton s Law in Cartesian Components 49
Newton s Law in Plane Polar Coordinates 50
The Physical Components of a Vector 51
The Christoffel Symbols 52
General Three Dimensional Coordinates 54
Newton s Law in General Coordinates 55
Computation of the Christoffel Symbols 58
An Alternative Formula for Computing the Christoffel Symbols 59
A Change of Coordinates 62
Transformation of the Christoffel Symbols 64
Exercises 65
CHAPTER IV
The Gradient, the Del Operator, Covariant Differentiation,
and the Divergence Theorem 71
The Gradient 71
Linear and Nonlinear Eigenvalue Problems 75
The Del Operator 76
The Divergence, Curl, and Gradient of a Vector Field 77
The Invariance of V • v, V x v, and Vv 78
The Covariant Derivative 79
The Component Forms of V ¦ v, V x v, and Vv 80
The Kinematics of Continuum Mechanics 81
The Divergence Theorem 83
Differential Geometry 87
Exercises 97
Index 107
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.63 |
| dewey-search | 515/.63 |
| dewey-sort | 3515 263 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-09T17:28:59Z |
| institution | BVB |
| isbn | 9780387940885 038794088X 354094088X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005977955 |
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| physical | XIV, 112 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series2 | Undergraduate texts in mathematics |
| spelling | Simmonds, James G. Verfasser aut A brief on tensor analysis James G. Simmonds 2. ed. New York u.a. Springer 1994 XIV, 112 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Tensoranalysis (DE-588)4204323-2 gnd rswk-swf Tensorrechnung (DE-588)4192487-3 gnd rswk-swf Tensoranalysis (DE-588)4204323-2 s DE-604 Tensorrechnung (DE-588)4192487-3 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005977955&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Simmonds, James G. A brief on tensor analysis Tensoranalysis (DE-588)4204323-2 gnd Tensorrechnung (DE-588)4192487-3 gnd |
| subject_GND | (DE-588)4204323-2 (DE-588)4192487-3 |
| title | A brief on tensor analysis |
| title_auth | A brief on tensor analysis |
| title_exact_search | A brief on tensor analysis |
| title_full | A brief on tensor analysis James G. Simmonds |
| title_fullStr | A brief on tensor analysis James G. Simmonds |
| title_full_unstemmed | A brief on tensor analysis James G. Simmonds |
| title_short | A brief on tensor analysis |
| title_sort | a brief on tensor analysis |
| topic | Tensoranalysis (DE-588)4204323-2 gnd Tensorrechnung (DE-588)4192487-3 gnd |
| topic_facet | Tensoranalysis Tensorrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005977955&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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