LEADER 04044nam 22006135 450 001 996418198203316 005 20200704143915.0 010 $a3-030-45193-3 024 7 $a10.1007/978-3-030-45193-6 035 $a(CKB)5310000000016627 035 $a(MiAaPQ)EBC6236142 035 $a(DE-He213)978-3-030-45193-6 035 $a(PPN)248598112 035 $a(EXLCZ)995310000000016627 100 $a20200623d2020 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDifferentiable Manifolds$b[electronic resource] $eA Theoretical Physics Approach /$fby Gerardo F. Torres del Castillo 205 $a2nd ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2020. 215 $a1 online resource (447 pages) 311 $a3-030-45192-5 327 $a1 Manifolds -- 2 Lie Derivatives -- 3 Differential Forms -- 4 Integral Manifolds -- 5 Connections -- 6. Riemannian Manifolds -- 7 Lie Groups -- 8 Hamiltonian Classical Mechanics -- Solutions -- References -- Index. 330 $aThis textbook gives a concise introduction to the theory of differentiable manifolds, focusing on their applications to differential equations, differential geometry, and Hamiltonian mechanics. The first three chapters introduce the basic concepts of the theory, such as differentiable maps, tangent vectors, vector and tensor fields, differential forms, local one-parameter groups of diffeomorphisms, and Lie derivatives. These tools are subsequently employed in the study of differential equations, connections, Riemannian manifolds, Lie groups, and Hamiltonian mechanics. Throughout, the book contains examples, worked out in detail, as well as exercises intended to show how the formalism is applied to actual computations and to emphasize the connections among various areas of mathematics. This second edition greatly expands upon the first by including more examples, additional exercises, and new topics, such as the moment map and fiber bundles. Detailed solutions to every exercise are also provided. Differentiable Manifolds is addressed to advanced undergraduate or beginning graduate students in mathematics or physics. Prerequisites include multivariable calculus, linear algebra, differential equations, and a basic knowledge of analytical mechanics Review of the first edition: This book presents an introduction to differential geometry and the calculus on manifolds with a view on some of its applications in physics. ? The present author has succeeded in writing a book which has its own flavor and its own emphasis, which makes it certainly a valuable addition to the literature on the subject. Frans Cantrijn, Mathematical Reviews. 606 $aDifferential geometry 606 $aPhysics 606 $aTopological groups 606 $aLie groups 606 $aMechanics 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 606 $aClassical Mechanics$3https://scigraph.springernature.com/ontologies/product-market-codes/P21018 615 0$aDifferential geometry. 615 0$aPhysics. 615 0$aTopological groups. 615 0$aLie groups. 615 0$aMechanics. 615 14$aDifferential Geometry. 615 24$aMathematical Methods in Physics. 615 24$aTopological Groups, Lie Groups. 615 24$aClassical Mechanics. 676 $a516.36 700 $aTorres del Castillo$b Gerardo F$4aut$4http://id.loc.gov/vocabulary/relators/aut$0768202 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418198203316 996 $aDifferentiable Manifolds$91936217 997 $aUNISA