語系:
繁體中文
English
說明(常見問題)
登入
回首頁
切換:
標籤
|
MARC模式
|
ISBD
Fundamentals of tensor calculus for ...
~
SpringerLink (Online service)
Fundamentals of tensor calculus for engineers with a primer on smooth manifolds
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Fundamentals of tensor calculus for engineers with a primer on smooth manifolds/ by Uwe Muhlich.
作者:
Muhlich, Uwe.
出版者:
Cham :Springer International Publishing : : 2017.,
面頁冊數:
xii, 125 p. :ill., digital ; : 24 cm.;
Contained By:
Springer eBooks
標題:
Calculus of tensors. -
電子資源:
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)
筆 0 讀者評論
多媒體
評論
新增評論
分享你的心得
Export
取書館別
處理中
...
變更密碼[密碼必須為2種組合(英文和數字)及長度為10碼以上]
登入