Tensor analysis with applications in mechanics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Singapore ; Hackensack, NJ
World Scientific
2010
|
| Edition: | [New ed.] |
| Subjects: | |
| Item Description: | Print version record |
| Physical Description: | 1 online resource (xiv, 363 pages) illustrations |
| ISBN: | 9789814313995 9814313998 |
Staff View
MARC
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| 100 | 1 | |a Lebedev, L. P. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Tensor analysis with applications in mechanics |c Leonid P. Lebedev, Michael J. Cloud, Victor A. Eremeyev |
| 250 | |a [New ed.] | ||
| 264 | 1 | |a Singapore ; Hackensack, NJ |b World Scientific |c 2010 | |
| 300 | |a 1 online resource (xiv, 363 pages) |b illustrations | ||
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| 338 | |b cr |2 rdacarrier | ||
| 500 | |a Print version record | ||
| 505 | 8 | |a "The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions. A tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. This book is a clear, concise, and self-contained treatment of tensors, tensor fields, and their applications. The book contains practically all the material on tensors needed for applications. It shows how this material is applied in mechanics, covering the foundations of the linear theories of elasticity and elastic shells. The main results are all presented in the first four chapters. The remainder of the book shows how one can apply these results to differential geometry and the study of various types of objects in continuum mechanics such as elastic bodies, plates, and shells. Each chapter of this new edition is supplied with exercises and problems - most with solutions, hints, or answers to help the reader progress. An extended appendix serves as a handbook-style summary of all important formulas contained in the book"--Provided by publisher | |
| 650 | 7 | |a MATHEMATICS / Vector Analysis |2 bisacsh | |
| 650 | 7 | |a Calculus of tensors |2 fast | |
| 650 | 7 | |a Civil & Environmental Engineering |2 hilcc | |
| 650 | 7 | |a Engineering & Applied Sciences |2 hilcc | |
| 650 | 7 | |a Operations Research |2 hilcc | |
| 650 | 4 | |a Calculus of tensors | |
| 700 | 1 | |a Cloud, Michael J. |e Sonstige |4 oth | |
| 700 | 1 | |a Eremeyev, Victor A. |e Sonstige |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |a Lebedev, L.P. |t Tensor analysis with applications in mechanics |b [New ed.] |d Singapore ; Hackensack, NJ : World Scientific, 2010 |z 9789814313124 |
| 912 | |a ZDB-4-ENC | ||
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-030730921 | |
Record in the Search Index
| _version_ | 1818984791433805824 |
|---|---|
| any_adam_object | |
| author | Lebedev, L. P. |
| author_facet | Lebedev, L. P. |
| author_role | aut |
| author_sort | Lebedev, L. P. |
| author_variant | l p l lp lpl |
| building | Verbundindex |
| bvnumber | BV045344217 |
| collection | ZDB-4-ENC |
| contents | "The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions. A tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. This book is a clear, concise, and self-contained treatment of tensors, tensor fields, and their applications. The book contains practically all the material on tensors needed for applications. It shows how this material is applied in mechanics, covering the foundations of the linear theories of elasticity and elastic shells. The main results are all presented in the first four chapters. The remainder of the book shows how one can apply these results to differential geometry and the study of various types of objects in continuum mechanics such as elastic bodies, plates, and shells. Each chapter of this new edition is supplied with exercises and problems - most with solutions, hints, or answers to help the reader progress. An extended appendix serves as a handbook-style summary of all important formulas contained in the book"--Provided by publisher |
| ctrlnum | (ZDB-4-ENC)ocn696298097 (OCoLC)696298097 (DE-599)BVBBV045344217 |
| dewey-full | 515/.63 |
| 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 | [New ed.] |
| format | Electronic eBook |
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| id | DE-604.BV045344217 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T18:24:37Z |
| institution | BVB |
| isbn | 9789814313995 9814313998 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030730921 |
| oclc_num | 696298097 |
| open_access_boolean | |
| physical | 1 online resource (xiv, 363 pages) illustrations |
| psigel | ZDB-4-ENC |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Lebedev, L. P. Verfasser aut Tensor analysis with applications in mechanics Leonid P. Lebedev, Michael J. Cloud, Victor A. Eremeyev [New ed.] Singapore ; Hackensack, NJ World Scientific 2010 1 online resource (xiv, 363 pages) illustrations txt rdacontent c rdamedia cr rdacarrier Print version record "The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions. A tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. This book is a clear, concise, and self-contained treatment of tensors, tensor fields, and their applications. The book contains practically all the material on tensors needed for applications. It shows how this material is applied in mechanics, covering the foundations of the linear theories of elasticity and elastic shells. The main results are all presented in the first four chapters. The remainder of the book shows how one can apply these results to differential geometry and the study of various types of objects in continuum mechanics such as elastic bodies, plates, and shells. Each chapter of this new edition is supplied with exercises and problems - most with solutions, hints, or answers to help the reader progress. An extended appendix serves as a handbook-style summary of all important formulas contained in the book"--Provided by publisher MATHEMATICS / Vector Analysis bisacsh Calculus of tensors fast Civil & Environmental Engineering hilcc Engineering & Applied Sciences hilcc Operations Research hilcc Calculus of tensors Cloud, Michael J. Sonstige oth Eremeyev, Victor A. Sonstige oth Erscheint auch als Druck-Ausgabe Lebedev, L.P. Tensor analysis with applications in mechanics [New ed.] Singapore ; Hackensack, NJ : World Scientific, 2010 9789814313124 |
| spellingShingle | Lebedev, L. P. Tensor analysis with applications in mechanics "The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions. A tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. This book is a clear, concise, and self-contained treatment of tensors, tensor fields, and their applications. The book contains practically all the material on tensors needed for applications. It shows how this material is applied in mechanics, covering the foundations of the linear theories of elasticity and elastic shells. The main results are all presented in the first four chapters. The remainder of the book shows how one can apply these results to differential geometry and the study of various types of objects in continuum mechanics such as elastic bodies, plates, and shells. Each chapter of this new edition is supplied with exercises and problems - most with solutions, hints, or answers to help the reader progress. An extended appendix serves as a handbook-style summary of all important formulas contained in the book"--Provided by publisher MATHEMATICS / Vector Analysis bisacsh Calculus of tensors fast Civil & Environmental Engineering hilcc Engineering & Applied Sciences hilcc Operations Research hilcc Calculus of tensors |
| title | Tensor analysis with applications in mechanics |
| title_auth | Tensor analysis with applications in mechanics |
| title_exact_search | Tensor analysis with applications in mechanics |
| title_full | Tensor analysis with applications in mechanics Leonid P. Lebedev, Michael J. Cloud, Victor A. Eremeyev |
| title_fullStr | Tensor analysis with applications in mechanics Leonid P. Lebedev, Michael J. Cloud, Victor A. Eremeyev |
| title_full_unstemmed | Tensor analysis with applications in mechanics Leonid P. Lebedev, Michael J. Cloud, Victor A. Eremeyev |
| title_short | Tensor analysis with applications in mechanics |
| title_sort | tensor analysis with applications in mechanics |
| topic | MATHEMATICS / Vector Analysis bisacsh Calculus of tensors fast Civil & Environmental Engineering hilcc Engineering & Applied Sciences hilcc Operations Research hilcc Calculus of tensors |
| topic_facet | MATHEMATICS / Vector Analysis Calculus of tensors Civil & Environmental Engineering Engineering & Applied Sciences Operations Research |
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