LEADER 04052nam 22006495 450 001 9910254333603321 005 20220415211755.0 010 $a3-319-56264-9 024 7 $a10.1007/978-3-319-56264-3 035 $a(CKB)3710000001177352 035 $a(DE-He213)978-3-319-56264-3 035 $a(MiAaPQ)EBC4843566 035 $a(PPN)200512218 035 $a(EXLCZ)993710000001177352 100 $a20170418d2017 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFundamentals of tensor calculus for engineers with a primer on smooth manifolds /$fby Uwe Mühlich 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XII, 125 p. 23 illus.) 225 1 $aSolid Mechanics and Its Applications,$x0925-0042 ;$v230 311 $a3-319-56263-0 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $a1 Introduction -- 2 Notes on point set topology -- 3 The ?nite dimensional real vector space -- 4 Tensor Algebra -- 5 Af?ne space and euclidean space -- 6 Tensor analysis in euclidean space -- 7 A primer on smooth manifolds -- B Further Reading. 330 $aThis book presents the fundamentals of modern tensor calculus for students in engineering and applied physics, emphasizing those aspects that are crucial for applying tensor calculus safely in Euclidian space and for grasping the very essence of the smooth manifold concept. After introducing the subject, it provides a brief exposition on point set topology to familiarize readers with the subject, especially with those topics required in later chapters. It then describes the finite dimensional real vector space and its dual, focusing on the usefulness of the latter for encoding duality concepts in physics. Moreover, it introduces tensors as objects that encode linear mappings and discusses affine and Euclidean spaces. Tensor analysis is explored first in Euclidean space, starting from a generalization of the concept of differentiability and proceeding towards concepts such as directional derivative, covariant derivative and integration based on differential forms. The final chapter addresses the role of smooth manifolds in modeling spaces other than Euclidean space, particularly the concepts of smooth atlas and tangent space, which are crucial to understanding the topic. Two of the most important concepts, namely the tangent bundle and the Lie derivative, are subsequently worked out. 410 0$aSolid Mechanics and Its Applications,$x0925-0042 ;$v230 606 $aMechanics 606 $aMechanics, Applied 606 $aContinuum physics 606 $aMathematical physics 606 $aPhysics 606 $aSolid Mechanics$3https://scigraph.springernature.com/ontologies/product-market-codes/T15010 606 $aClassical and Continuum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P2100X 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 615 0$aMechanics. 615 0$aMechanics, Applied. 615 0$aContinuum physics. 615 0$aMathematical physics. 615 0$aPhysics. 615 14$aSolid Mechanics. 615 24$aClassical and Continuum Physics. 615 24$aMathematical Applications in the Physical Sciences. 615 24$aMathematical Methods in Physics. 676 $a515.63 700 $aMühlich$b Uwe$4aut$4http://id.loc.gov/vocabulary/relators/aut$0929363 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254333603321 996 $aFundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds$92088786 997 $aUNINA