Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds (Record no. 81053)
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000 -LEADER | |
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fixed length control field | 03579nam a22005655i 4500 |
001 - CONTROL NUMBER | |
control field | 978-3-319-56264-3 |
005 - DATE AND TIME OF LATEST TRANSACTION | |
control field | 20220801222707.0 |
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
fixed length control field | 170418s2017 sz | s |||| 0|eng d |
020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
ISBN | 9783319562643 |
-- | 978-3-319-56264-3 |
082 04 - CLASSIFICATION NUMBER | |
Call Number | 620.105 |
100 1# - AUTHOR NAME | |
Author | Mühlich, Uwe. |
245 10 - TITLE STATEMENT | |
Title | Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds |
250 ## - EDITION STATEMENT | |
Edition statement | 1st ed. 2017. |
300 ## - PHYSICAL DESCRIPTION | |
Number of Pages | XII, 125 p. 23 illus. |
490 1# - SERIES STATEMENT | |
Series statement | Solid Mechanics and Its Applications, |
505 0# - FORMATTED CONTENTS NOTE | |
Remark 2 | 1 Introduction -- 2 Notes on point set topology -- 3 The finite dimensional real vector space -- 4 Tensor Algebra -- 5 Affine space and euclidean space -- 6 Tensor analysis in euclidean space -- 7 A primer on smooth manifolds -- B Further Reading. |
520 ## - SUMMARY, ETC. | |
Summary, etc | This book presents the fundamentals of modern tensor calculus for students in engineering and applied physics, emphasizing those aspects that are crucial for applying tensor calculus safely in Euclidian space and for grasping the very essence of the smooth manifold concept. After introducing the subject, it provides a brief exposition on point set topology to familiarize readers with the subject, especially with those topics required in later chapters. It then describes the finite dimensional real vector space and its dual, focusing on the usefulness of the latter for encoding duality concepts in physics. Moreover, it introduces tensors as objects that encode linear mappings and discusses affine and Euclidean spaces. Tensor analysis is explored first in Euclidean space, starting from a generalization of the concept of differentiability and proceeding towards concepts such as directional derivative, covariant derivative and integration based on differential forms. The final chapter addresses the role of smooth manifolds in modeling spaces other than Euclidean space, particularly the concepts of smooth atlas and tangent space, which are crucial to understanding the topic. Two of the most important concepts, namely the tangent bundle and the Lie derivative, are subsequently worked out. |
856 40 - ELECTRONIC LOCATION AND ACCESS | |
Uniform Resource Identifier | https://doi.org/10.1007/978-3-319-56264-3 |
942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
Koha item type | eBooks |
264 #1 - | |
-- | Cham : |
-- | Springer International Publishing : |
-- | Imprint: Springer, |
-- | 2017. |
336 ## - | |
-- | text |
-- | txt |
-- | rdacontent |
337 ## - | |
-- | computer |
-- | c |
-- | rdamedia |
338 ## - | |
-- | online resource |
-- | cr |
-- | rdacarrier |
347 ## - | |
-- | text file |
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-- | rda |
650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
-- | Mechanics, Applied. |
650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
-- | Solids. |
650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
-- | Physics. |
650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
-- | Mathematical physics. |
650 14 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
-- | Solid Mechanics. |
650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
-- | Classical and Continuum Physics. |
650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
-- | Mathematical Physics. |
650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
-- | Mathematical Methods in Physics. |
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
-- | 2214-7764 ; |
912 ## - | |
-- | ZDB-2-ENG |
912 ## - | |
-- | ZDB-2-SXE |
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