國立虎尾科技大學 |

Fundamentals of tensor calculus for engineers with a primer on smooth manifolds

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Fundamentals of tensor calculus for engineers with a primer on smooth manifolds/ by Uwe Muhlich.
Author:	Muhlich, Uwe.
Published:	Cham :Springer International Publishing : : 2017.,
Description:	xii, 125 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Calculus of tensors. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-56264-3
ISBN:	9783319562643

Fundamentals of tensor calculus for engineers with a primer on smooth manifolds
Muhlich, Uwe.

Fundamentals of tensor calculus for engineers with a primer on smooth manifolds[electronic resource] /by Uwe Muhlich. - Cham :Springer International Publishing :2017. - xii, 125 p. :ill., digital ;24 cm. - Solid mechanics and its applications,v.2300925-0042 ;. - Solid mechanics and its applications ;v. 136.

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.

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.

ISBN: 9783319562643

Standard No.: 10.1007/978-3-319-56264-3doiSubjects--Topical Terms:

598495
Calculus of tensors.

LC Class. No.: QA433

Dewey Class. No.: 515.63

Fundamentals of tensor calculus for engineers with a primer on smooth manifolds
LDR:02598nam a2200337 a 4500 001 884805
003 DE-He213
005 20171116173602.0
006 m d
007 cr nn 008maaau
008 180530s2017 gw s 0 eng d
020 $a 9783319562643 $q (electronic bk.)
020 $a 9783319562636 $q (paper)
024 7 $a 10.1007/978-3-319-56264-3 $2 doi
035 $a 978-3-319-56264-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA433
072 7 $a TG $2 bicssc
072 7 $a TEC009070 $2 bisacsh
072 7 $a TEC021000 $2 bisacsh
082 0 4 $a 515.63 $2 23
090 $a QA433 $b .M952 2017
100 1 $a Muhlich, Uwe. $3 1141496
245 1 0 $a Fundamentals of tensor calculus for engineers with a primer on smooth manifolds $h [electronic resource] / $c by Uwe Muhlich.
260 $a Cham : $c 2017. $b Springer International Publishing : $b Imprint: Springer,
300 $a xii, 125 p. : $b ill., digital ; $c 24 cm.
490 1 $a Solid mechanics and its applications, $x 0925-0042 ; $v v.230
505 0 $a 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 $a 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.
650 0 $a Calculus of tensors. $3 598495
650 0 $a Manifolds (Mathematics) $3 672402
650 1 4 $a Engineering. $3 561152
650 2 4 $a Continuum Mechanics and Mechanics of Materials. $3 670886
650 2 4 $a Classical and Continuum Physics. $3 1141497
650 2 4 $a Mathematical Applications in the Physical Sciences. $3 786649
650 2 4 $a Mathematical Methods in Physics. $3 670749
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Solid mechanics and its applications ; $v v. 136 $3 761836
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-56264-3
950 $a Engineering (Springer-11647)