Tensor calculus with applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore
World Scientific
2003
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 367 S. |
| ISBN: | 9812385061 |
Staff View
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Record in the Search Index
| _version_ | 1804130511468101632 |
|---|---|
| adam_text | MAKS A. AKIVIS JERUSALEM INSTITUTE OF TECHNOLOGY, ISRAEL VLADISLAV V.
GOLDBERG NEW JERSEY INSTITUTE OF TECHNOLOGY, USA TENSOR CALCULUS WITH
APPLICATIONS TRANSLATED FROM RUSSIAN BY VLADISLAV V. GOLDBERG WORLD
SCIENTIFIC NEW JERSEY * LONDON * SINGAPORE * HONG KONG CONTENTS
TRANSLATOR S INTRODUCTION IX PREFACE TO THE RUSSIAN EDITION XI CHAPTER 1
VECTOR SPACES 1 1.1 CONCEPT OF A VECTOR SPACE 1 1.2 LINEAR DEPENDENCE OF
VECTORS 4 1.3 DIMENSION AND BASIS OF A VECTOR SPACE 9 1.4 ORTHONORMAL
BASES IN A THREE-DIMENSIONAL SPACE. THE SCALAR PRODUCT OF VECTORS 13 1.5
THE VECTOR PRODUCT AND TRIPLE PRODUCTS OF VECTORS 19 1.6 TRANSFORMATIONS
OF ORTHONORMAL BASIS. FUNDAMENTAL PROBLEM OF TENSOR CALCULUS 26 1.7 SOME
TOPICS IN THREE-DIMENSIONAL ANALYTIC GEOMETRY 35 CHAPTER 2 MULTILINEAR
FORMS AND TENSORS 45 2.1 LINEAR FORMS 45 2.2 BILINEAR FORMS 48 2.3
MULTILINEAR FORMS. GENERAL DEFINITION OF A TENSOR 52 2.4 ALGEBRAIC
OPERATIONS ON TENSORS 59 2.5 SYMMETRIC AND ANTISYMMETRIC TENSORS 65
CHAPTER 3 LINEAR TRANSFORMATIONS AND SECOND-ORDER TENSORS 77 3.1 LINEAR
TRANSFORMATIONS 77 3.2 THE MATRIX OF A LINEAR TRANSFORMATION 82 3.3 THE
DETERMINANT OF THE MATRIX OF A LINEAR TRANSFORMATION. THE RANK OF A
MATRIX 89 3.4 LINEAR TRANSFORMATIONS AND BILINEAR FORMS 94 3.5
MULTIPLICATION OF LINEAR TRANSFORMATIONS AND MATRICES ... 105 3.6
INVERSE LINEAR TRANSFORMATIONS AND INVERSE MATRICES 113 3.7 THE GROUP OF
LINEAR TRANSFORMATIONS AND ITS SUBGROUPS . 118 VI CONTENTS CHAPTER 4
REDUCTION OF THE MATRIX OF LINEAR TRANSFORMATION TO THE SIMPLEST FORM
129 4.1 EIGENVECTORS AND EIGENVALUES OF A LINEAR TRANSFORMATION 129 4.2
REDUCTION OF THE MATRIX OF LINEAR TRANSFORMATION TO THE SIMPLEST FORM IN
THE CASE OF DISTINCT EIGENVALUES 141 4.3 MATRIX POLYNOMIALS AND THE
HAMILTON-CAYLEY THEOREM 146 4.4 PROPERTIES OF EIGENVECTORS AND
EIGENVALUES OF A SYMMETRIC LINEAR TRANSFORMATION 150 4.5 DIAGONALIZATION
OF THE MATRIX OF A SYMMETRIC LINEAR TRANSFORMATION 153 4.6 REDUCTION OF
A QUADRATIC FORM TO CANONICAL FORM 161 4.7 REPRESENTATION OF A
NONSINGULAR LINEAR TRANSFORMATION AS THE PRODUCT OF A SYMMETRIC
TRANSFORMATION AND AN ORTHOGONAL TRANSFORMATION 167 CHAPTER 5 THE
GENERAL THEORY OF SECOND-DEGREE SURFACES 173 5.1 GENERAL EQUATION OF A
SECOND-DEGREE SURFACE 173 5.2 REDUCTION OF THE GENERAL EQUATION OF
SECOND-DEGREE SURFACES TO THE SIMPLEST FORM 178 5.3 DETERMINATION OF THE
TYPE OF SECOND-DEGREE SURFACE BY MEANS OF ITS INVARIANTS 183 5.4
CLASSIFICATION OF SECOND-DEGREE SURFACES 188 5.5 APPLICATION OF THE
THEORY OF INVARIANTS TO CLASSIFICATION OF SECOND-DEGREE SURFACES 193 5.6
CENTRAL AND NONCENTRAL SECOND-DEGREE SURFACES 198 5.7 EXAMPLES 201
CHAPTER 6 APPLICATIONS OF TENSOR CALCULUS TO SOME PROBLEM OF MECHANICS
AND PHYSICS 211 6.1 THE INERTIA TENSOR 211 6.2 PROPERTIES OF CRYSTALS
CONNECTED WITH SECOND-ORDER 220 TENSORS 220 6.3 THE STRESS AND STRAIN
TENSORS 230 6.4 FURTHER PROPERTIES OF CRYSTALS 245 CONTENTS VII CHAPTER
7 FOUNDATIONS OF TENSOR ANALYSIS 259 7.1 TENSOR FIELDS AND THEIR
DIFFERENTIATION 259 7.2 MECHANICS OF A DEFORMABLE MEDIUM 274 7.3
ORTHOGONAL CURVILINEAR COORDINATE SYSTEMS 283 7.4 MOVING FRAME OF AN
ORTHOGONAL CURVILINEAR COORDINATE SYSTEM AND TENSOR FIELDS 293 7.5
DIFFERENTIATION OF A TENSOR FIELD IN CURVILINEAR COORDINATES 304
SELECTED ANSWERS AND HINTS 317 BIBLIOGRAPHY 345 INDEX 349
|
| any_adam_object | 1 |
| author | Akivis, Maks A. 1923- Golʹdberg, Vladislav V. 1936- |
| author_GND | (DE-588)128639601 (DE-588)128639644 |
| author_facet | Akivis, Maks A. 1923- Golʹdberg, Vladislav V. 1936- |
| author_role | aut aut |
| author_sort | Akivis, Maks A. 1923- |
| author_variant | m a a ma maa v v g vv vvg |
| building | Verbundindex |
| bvnumber | BV017820875 |
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| ctrlnum | (OCoLC)249122096 (DE-599)BVBBV017820875 |
| discipline | Mathematik |
| format | Book |
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| physical | XII, 367 S. |
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| publisher | World Scientific |
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| spelling | Akivis, Maks A. 1923- Verfasser (DE-588)128639601 aut Tensor calculus with applications by Maks A. Akivis ; Vladislav V. Goldberg Singapore World Scientific 2003 XII, 367 S. txt rdacontent n rdamedia nc rdacarrier Lehrbuch Tensoranalysis Tensorrechnung Tensorrechnung - Tensoranalysis Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Tensorrechnung (DE-588)4192487-3 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Lineare Algebra (DE-588)4035811-2 s 2\p DE-604 Tensorrechnung (DE-588)4192487-3 s 3\p DE-604 Golʹdberg, Vladislav V. 1936- Verfasser (DE-588)128639644 aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010697850&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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Akivis, Maks A. 1923- Golʹdberg, Vladislav V. 1936- Tensor calculus with applications Lehrbuch Tensoranalysis Tensorrechnung Tensorrechnung - Tensoranalysis Lineare Algebra (DE-588)4035811-2 gnd Tensorrechnung (DE-588)4192487-3 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4192487-3 (DE-588)4151278-9 |
| title | Tensor calculus with applications |
| title_auth | Tensor calculus with applications |
| title_exact_search | Tensor calculus with applications |
| title_full | Tensor calculus with applications by Maks A. Akivis ; Vladislav V. Goldberg |
| title_fullStr | Tensor calculus with applications by Maks A. Akivis ; Vladislav V. Goldberg |
| title_full_unstemmed | Tensor calculus with applications by Maks A. Akivis ; Vladislav V. Goldberg |
| title_short | Tensor calculus with applications |
| title_sort | tensor calculus with applications |
| topic | Lehrbuch Tensoranalysis Tensorrechnung Tensorrechnung - Tensoranalysis Lineare Algebra (DE-588)4035811-2 gnd Tensorrechnung (DE-588)4192487-3 gnd |
| topic_facet | Lehrbuch Tensoranalysis Tensorrechnung Tensorrechnung - Tensoranalysis Lineare Algebra Einführung |
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