Tensor algebra and tensor analysis for engineers: with applications to continuum mechanics
<p>There is a large gap between the engineering course in tensor algebra on the one hand and the treatment of linear transformations within classical linear algebra on the other hand. The aim of this modern textbook is to bridge this gap by means of the consequent and fundamental exposition. T...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2013
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Mathematical engineering
|
| Schlagworte: | |
| Online-Zugang: | BTU01 FHA01 FHI01 FHN01 FHR01 FKE01 FWS01 UBY01 Volltext Inhaltsverzeichnis Abstract |
| Zusammenfassung: | <p>There is a large gap between the engineering course in tensor algebra on the one hand and the treatment of linear transformations within classical linear algebra on the other hand. The aim of this modern textbook is to bridge this gap by means of the consequent and fundamental exposition. The book primarily addresses engineering students with some initial knowledge of matrix algebra. Thereby the mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises are provided in the book and are accompanied by solutions, enabling self-study. The last chapters of the book deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and are therefore of high interest for PhD-students and scientists working in this area.</p><p>This third edition is completed by a number of additional figures, examples and exercises. The text and formulae have been revised and improved where necessary.</p> |
| Beschreibung: | Vectors and Tensors in a Finite-Dimensional Space -- Vector and Tensor Analysis in Euclidean Space -- Curves and Surfaces in Three-Dimensional Euclidean Space -- Eigenvalue Problem and Spectral Decomposition of Second-Order Tensors -- Fourth-Order Tensors -- Analysis of Tensor Functions -- Analytic Tensor Functions -- Applications to Continuum Mechanics |
| Beschreibung: | 1 Online-Ressource (XV, 269 p. 17 illus) |
| ISBN: | 9783642308796 |
| DOI: | 10.1007/978-3-642-30879-6 |
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Datensatz im Suchindex
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| adam_text | TENSOR ALGEBRA AND TENSOR ANALYSIS FOR ENGINEERS
/ ITSKOV, MIKHAIL
: 2013
TABLE OF CONTENTS / INHALTSVERZEICHNIS
VECTORS AND TENSORS IN A FINITE-DIMENSIONAL SPACE
VECTOR AND TENSOR ANALYSIS IN EUCLIDEAN SPACE
CURVES AND SURFACES IN THREE-DIMENSIONAL EUCLIDEAN SPACE
EIGENVALUE PROBLEM AND SPECTRAL DECOMPOSITION OF SECOND-ORDER TENSORS
FOURTH-ORDER TENSORS
ANALYSIS OF TENSOR FUNCTIONS
ANALYTIC TENSOR FUNCTIONS
APPLICATIONS TO CONTINUUM MECHANICS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
TENSOR ALGEBRA AND TENSOR ANALYSIS FOR ENGINEERS
/ ITSKOV, MIKHAIL
: 2013
ABSTRACT / INHALTSTEXT
THERE IS A LARGE GAP BETWEEN THE ENGINEERING COURSE IN TENSOR ALGEBRA ON
THE ONE HAND AND THE TREATMENT OF LINEAR TRANSFORMATIONS WITHIN
CLASSICAL LINEAR ALGEBRA ON THE OTHER HAND. THE AIM OF THIS MODERN
TEXTBOOK IS TO BRIDGE THIS GAP BY MEANS OF THE CONSEQUENT AND
FUNDAMENTAL EXPOSITION. THE BOOK PRIMARILY ADDRESSES ENGINEERING
STUDENTS WITH SOME INITIAL KNOWLEDGE OF MATRIX ALGEBRA. THEREBY THE
MATHEMATICAL FORMALISM IS APPLIED AS FAR AS IT IS ABSOLUTELY NECESSARY.
NUMEROUS EXERCISES ARE PROVIDED IN THE BOOK AND ARE ACCOMPANIED BY
SOLUTIONS, ENABLINGSELF-STUDY. THE LAST CHAPTERS OF THE BOOK DEAL WITH
MODERN DEVELOPMENTS IN THE THEORY OF ISOTROPIC AND ANISOTROPIC TENSOR
FUNCTIONS AND THEIR APPLICATIONS TO CONTINUUM MECHANICS AND ARE
THEREFORE OF HIGH INTEREST FOR PHD-STUDENTS AND SCIENTISTS WORKING IN
THIS AREA. THIS THIRD EDITION IS COMPLETED BY A NUMBER OF ADDITIONAL
FIGURES, EXAMPLES AND EXERCISES. THE TEXT AND FORMULAEHAVE
BEENREVISED AND IMPROVED WHERE NECESSARY
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Itskov, Mikhail |
| author_facet | Itskov, Mikhail |
| author_role | aut |
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| author_variant | m i mi |
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| dewey-full | 620.1 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.1 |
| dewey-search | 620.1 |
| dewey-sort | 3620.1 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-30879-6 |
| edition | 3. ed. |
| format | Electronic eBook |
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| spellingShingle | Itskov, Mikhail Tensor algebra and tensor analysis for engineers with applications to continuum mechanics Ingenieurwissenschaften Engineering Matrix theory Global differential geometry Mechanics Materials Tensoranalysis (DE-588)4204323-2 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Tensoralgebra (DE-588)4505278-5 gnd Tensorrechnung (DE-588)4192487-3 gnd |
| subject_GND | (DE-588)4204323-2 (DE-588)4137304-2 (DE-588)4505278-5 (DE-588)4192487-3 |
| 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 | Ingenieurwissenschaften Engineering Matrix theory Global differential geometry Mechanics Materials Tensoranalysis (DE-588)4204323-2 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Tensoralgebra (DE-588)4505278-5 gnd Tensorrechnung (DE-588)4192487-3 gnd |
| topic_facet | Ingenieurwissenschaften Engineering Matrix theory Global differential geometry Mechanics Materials Tensoranalysis Tensoralgebra Tensorrechnung |
| url | https://doi.org/10.1007/978-3-642-30879-6 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025869088&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025869088&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT itskovmikhail tensoralgebraandtensoranalysisforengineerswithapplicationstocontinuummechanics |