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LEADER 00000cam a2200613Ii 4500 
003    OCoLC 
005    20190319060824.4 
006    m     o  d         
007    cr cnu|||unuuu 
008    170420s2017    sz      ob    001 0 eng d 
015    GBB8N7645|2bnb 
019    SpringerEBAocn983204384 
020    9783319562643|q(electronic bk.) 
020    3319562649|q(electronic bk.) 
020    |z9783319562636|q(print) 
020    |z3319562630 
024 7  10.1007/978-3-319-56264-3|2doi 
037    com.springer.onix.9783319562643|bSpringer Nature 
040    N$T|beng|erda|epn|cN$T|dEBLCP|dN$T|dGW5XE|dYDX|dOCLCF|dAZU
       |dUPM|dVT2|dMERER|dOCLCQ|dIDB|dMERUC|dUAB|dIOG|dU3W|dCAUOI
       |dOCLCQ|dKSU|dEZ9|dAU@|dESU|dWYU|dOCLCQ|dLVT|dUKMGB 
049    MAIN 
050  4 QA433 
066    |c(S 
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. 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
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
       Manifolds. 
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 
       Problems; Index. 
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
       |z9783319562636|w(OCoLC)973914631 
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://
       link.springer.com/10.1007/978-3-319-56264-3|zConnect to 
       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 
990    Batch Ebook load (bud2) - do not edit, delete or attach 
       any records. 
991    |zNEW New collection springerlink.ebooksengine2017 2019-03
       -18 
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