Tensor algebra and tensor analysis for engineers: with applications to continuum mechanics
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2009
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 247 S. graph. Darst. |
| ISBN: | 9783540939061 |
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MARC
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| 245 | 1 | 0 | |a Tensor algebra and tensor analysis for engineers |b with applications to continuum mechanics |c Mikhail Itskov |
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Record in the Search Index
| _version_ | 1804139386776846336 |
|---|---|
| adam_text | CONTENTS VECTORS AND TENSORS IN A FINITE-DIMENSIONAL SPACE 1 1.1 NOTION
OF THE VECTOR SPACE 1 1.2 BASIS AND DIMENSION OF THE VECTOR SPACE 3 1.3
COMPONENTS OF A VECTOR, SUMMATION CONVENTION 5 1.4 SCALAR PRODUCT,
EUCLIDEAN SPACE, ORTHONORMAL BASIS 6 1.5 DUAL BASES 8 1.6 SECOND-ORDER
TENSOR AS A LINEAR MAPPING 12 1.7 TENSOR PRODUCT, REPRESENTATION OF A
TENSOR WITH RESPECT TO A BASIS 16 1.8 CHANGE OF THE BASIS,
TRANSFORMATION RULES 19 1.9 SPECIAL OPERATIONS WITH SECOND-ORDER TENSORS
20 1.10 SCALAR PRODUCT OF SECOND-ORDER TENSORS 26 1.11 DECOMPOSITIONS OF
SECOND-ORDER TENSORS 27 1.12 TENSORS OF HIGHER ORDERS 29 EXERCISES 30
VECTOR AND TENSOR ANALYSIS IN EUCLIDEAN SPACE 35 2.1 VECTOR- AND
TENSOR-VALUED FUNCTIONS, DIFFERENTIAL CALCULUS ... 35 2.2 COORDINATES IN
EUCLIDEAN SPACE, TANGENT VECTORS 37 2.3 COORDINATE TRANSFORMATION. CO-,
CONTRA- AND MIXED VARIANT COMPONENTS 40 2.4 GRADIENT, COVARIANT AND
CONTRAVARIANT DERIVATIVES 42 2.5 CHRISTOFFEL SYMBOLS, REPRESENTATION OF
THE COVARIANT DERIVATIVE 46 2.6 APPLICATIONS IN THREE-DIMENSIONAL SPACE:
DIVERGENCE AND CURL 49 EXERCISES 57 CURVES AND SURFACES IN
THREE-DIMENSIONAL EUCLIDEAN SPACE 59 3.1 CURVES IN THREE-DIMENSIONAL
EUCLIDEAN SPACE 59 3.2 SURFACES IN THREE-DIMENSIONAL EUCLIDEAN SPACE 66
3.3 APPLICATION TO SHELL THEORY 73 EXERCISE BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/992998786 DIGITALISIERT DURCH XII
CONTENTS 4 EIGENVALUE PROBLEM AND SPECTRAL DECOMPOSITION OF SECOND-ORDER
TENSORS 81 4.1 COMPLEXIFICATION 81 4.2 EIGENVALUE PROBLEM, EIGENVALUES
AND EIGENVECTORS 82 4.3 CHARACTERISTIC POLYNOMIAL 85 4.4 SPECTRAL
DECOMPOSITION AND EIGENPROJECTIONS 87 4.5 SPECTRAL DECOMPOSITION OF
SYMMETRIC SECOND-ORDER TENSORS .. 92 4.6 SPECTRAL DECOMPOSITION OF
ORTHOGONAL AND SKEW-SYMMETRIC SECOND-ORDER TENSORS 94 4.7
CAYLEY-HAMILTON THEOREM 98 EXERCISES 100 5 FOURTH-ORDER TENSORS 103 5.1
FOURTH-ORDER TENSORS AS A LINEAR MAPPING 103 5.2 TENSOR PRODUCTS,
REPRESENTATION OF FOURTH-ORDER TENSORS WITH RESPECT TO A BASIS 104 5.3
SPECIAL OPERATIONS WITH FOURTH-ORDER TENSORS 106 5.4 SUPER-SYMMETRIC
FOURTH-ORDER TENSORS 109 5.5 SPECIAL FOURTH-ORDER TENSORS ILL EXERCISES
114 6 ANALYSIS OF TENSOR FUNCTIONS 115 6.1 SCALAR-VALUED ISOTROPIE
TENSOR FUNCTIONS 115 6.2 SCALAR-VALUED ANISOTROPIE TENSOR FUNCTIONS 119
6.3 DERIVATIVES OF SCALAR-VALUED TENSOR FUNCTIONS 122 6.4 TENSOR-VALUED
ISOTROPIE AND ANISOTROPIE TENSOR FUNCTIONS .... 129 6.5 DERIVATIVES OF
TENSOR-VALUED TENSOR FUNCTIONS 135 6.6 GENERALIZED RIVLIN S IDENTITIES
140 EXERCISES 142 7 ANALYTIC TENSOR FUNCTIONS 145 7.1 INTRODUCTION 145
7.2 CLOSED-FORM REPRESENTATION FOR ANALYTIC TENSOR FUNCTIONS AN CONTENTS
XIII 8.4 TIME RATE OF GENERALIZED STRAINS 173 8.5 STRESS CONJUGATE TO A
GENERALIZED STRAIN 175 8.6 FINITE PLASTICITY BASED ON THE ADDITIVE
DECOMPOSITION OF GENERALIZED STRAINS 178 EXERCISES 182 SOLUTIONS 185
REFERENCES 239 INDEX 243
|
| any_adam_object | 1 |
| author | Itskov, Mikhail |
| author_facet | Itskov, Mikhail |
| author_role | aut |
| author_sort | Itskov, Mikhail |
| author_variant | m i mi |
| building | Verbundindex |
| bvnumber | BV035680479 |
| classification_rvk | SK 370 |
| classification_tum | MAT 157f MAT 535f |
| ctrlnum | (OCoLC)404008096 (DE-599)BVBBV035680479 |
| dewey-full | 515.3602462 512.5702462 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis 512 - Algebra |
| dewey-raw | 515.3602462 512.5702462 |
| dewey-search | 515.3602462 512.5702462 |
| dewey-sort | 3515.3602462 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV035680479 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:43:16Z |
| institution | BVB |
| isbn | 9783540939061 |
| language | English |
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| owner_facet | DE-29T DE-703 DE-1047 |
| physical | XIII, 247 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| spelling | Itskov, Mikhail Verfasser aut Tensor algebra and tensor analysis for engineers with applications to continuum mechanics Mikhail Itskov 2. ed. Berlin [u.a.] Springer 2009 XIII, 247 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Tensorrechnung (DE-588)4192487-3 gnd rswk-swf Tensoranalysis (DE-588)4204323-2 gnd rswk-swf Tensoralgebra (DE-588)4505278-5 gnd rswk-swf Ingenieurwissenschaften (DE-588)4137304-2 gnd rswk-swf Tensorrechnung (DE-588)4192487-3 s DE-604 Ingenieurwissenschaften (DE-588)4137304-2 s Tensoranalysis (DE-588)4204323-2 s 1\p DE-604 Tensoralgebra (DE-588)4505278-5 s 2\p DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017734751&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Itskov, Mikhail Tensor algebra and tensor analysis for engineers with applications to continuum mechanics Tensorrechnung (DE-588)4192487-3 gnd Tensoranalysis (DE-588)4204323-2 gnd Tensoralgebra (DE-588)4505278-5 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd |
| subject_GND | (DE-588)4192487-3 (DE-588)4204323-2 (DE-588)4505278-5 (DE-588)4137304-2 |
| title | Tensor algebra and tensor analysis for engineers with applications to continuum mechanics |
| title_auth | Tensor algebra and tensor analysis for engineers with applications to continuum mechanics |
| title_exact_search | Tensor algebra and tensor analysis for engineers with applications to continuum mechanics |
| title_full | Tensor algebra and tensor analysis for engineers with applications to continuum mechanics Mikhail Itskov |
| title_fullStr | Tensor algebra and tensor analysis for engineers with applications to continuum mechanics Mikhail Itskov |
| title_full_unstemmed | Tensor algebra and tensor analysis for engineers with applications to continuum mechanics Mikhail Itskov |
| title_short | Tensor algebra and tensor analysis for engineers |
| title_sort | tensor algebra and tensor analysis for engineers with applications to continuum mechanics |
| title_sub | with applications to continuum mechanics |
| topic | Tensorrechnung (DE-588)4192487-3 gnd Tensoranalysis (DE-588)4204323-2 gnd Tensoralgebra (DE-588)4505278-5 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd |
| topic_facet | Tensorrechnung Tensoranalysis Tensoralgebra Ingenieurwissenschaften |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017734751&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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