LEADER 00000cam a2200613Ii 4500
006 m o d
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008 170420s2017 sz ob 001 0 eng d
020 9783319562643|q(electronic bk.)
020 3319562649|q(electronic bk.)
024 7 10.1007/978-3-319-56264-3|2doi
037 com.springer.onix.9783319562643|bSpringer Nature
050 4 QA433
082 04 515/.63|223
082 04 620
100 1 Mühlich, Uwe,|eauthor.
245 10 Fundamentals of tensor calculus for engineers with a
primer on smooth manifolds /|cUwe Mühlich.
264 1 Cham, Switzerland :|bSpringer,|c2017.
300 1 online resource.
338 online resource|bcr|2rdacarrier
347 text file|bPDF|2rda
490 1 Solid mechanics and its applications ;|vvolume 230
504 Includes bibliographical references and index.
505 0 |6880-01|aPreface; Acknowledgements; Contents; Selected
Symbols; 1 Introduction; 1.1 Space, Geometry, and Linear
Algebra; 1.2 Vectors as Geometrical Objects; 1.3
Differentiable Manifolds: First Contact; 1.4 Digression on
Notation and Mappings; References; 2 Notes on Point Set
Topology; 2.1 Preliminary Remarks and Basic Concepts; 2.2
Topology in Metric Spaces; 2.3 Topological Space:
Definition and Basic Notions; 2.4 Connectedness,
Compactness, and Separability; 2.5 Product Spaces and
Product Topologies; 2.6 Further Reading; References; 3 The
Finite-Dimensional Real Vector Space; 3.1 Definitions.
505 8 3.2 Linear Independence and Basis3.3 Some Common Examples
for Vector Spaces; 3.4 Change of Basis; 3.5 Linear
Mappings Between Vector Spaces; 3.6 Linear Forms and the
Dual Vector Space; 3.7 The Inner Product, Norm, and
Metric; 3.8 The Reciprocal Basis and Its Relations with
the Dual Basis; References; 4 Tensor Algebra; 4.1 Tensors
and Multi-linear Forms; 4.2 Dyadic Product and Tensor
Product Spaces; 4.3 The Dual of a Linear Mapping; 4.4
Remarks on Notation and Inner Product Operations; 4.5 The
Exterior Product and Alternating Multi-linear Forms; 4.6
Symmetric and Skew-Symmetric Tensors.
505 8 6.3 Gradient of a Scalar Field and Related Concepts in
mathbbRN6.4 Differentiability in Euclidean Space Supposing
Affine Relations; 6.5 Characteristic Features of Nonlinear
Chart Relations; 6.6 Partial Derivatives as Vectors and
Tangent Space at a Point; 6.7 Curvilinear Coordinates and
Covariant Derivative; 6.8 Differential Forms in mathbbRN
and Integration; 6.9 Exterior Derivative and Stokes'
Theorem in Form Language; References; 7 A Primer on Smooth
Manifolds; 7.1 Introduction; 7.2 Basic Concepts Regarding
Analysis on Surfaces in mathbbR3; 7.3 Transition to Smooth
505 8 7.4 Tangent Bundle and Vector Fields7.5 Flow of Vector
Fields and the Lie Derivative; 7.6 Outlook and Further
Reading; References; Appendix Solutions for Selected
520 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 Calculus of tensors.
650 0 Manifolds (Mathematics)
655 4 Electronic books.
710 2 SpringerLink|eissuing body.
776 08 |iPrint version:|aMühlich, Uwe.|tFundamentals of tensor
calculus for engineers with a primer on smooth manifolds.
|dCham, Switzerland : Springer, 2017|z3319562630
830 0 Solid mechanics and its applications ;|vv. 230.
830 0 Springer Engineering eBooks 2017 English+International
856 40 |uhttps://ezp.lib.unimelb.edu.au/login?url=http://
ebook (University of Melbourne only)
880 8 |6505-01/(S|a4.7 Generalized Kronecker Symbol4.8 The
Spaces Λk mathcalV and Λk mathcalV*; 4.9 Properties of the
Exterior Product and the Star-Operator; 4.10 Relation with
Classical Linear Algebra; References; 5 Affine Space and
Euclidean Space; 5.1 Definitions and Basic Notions; 5.2
Alternative Definition of an Affine Space by Hybrid
Addition; 5.3 Affine Mappings, Coordinate Charts and
Topological Aspects; References; 6 Tensor Analysis in
Euclidean Space; 6.1 Differentiability in mathbbR and
Related Concepts Briefly Revised; 6.2 Generalization of
the Concept of Differentiability.
990 Springer EBA e-book collections for 2017-2019
990 Springer Engineering 2017
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