04044nam 22006135 450 99641819820331620200704143915.03-030-45193-310.1007/978-3-030-45193-6(CKB)5310000000016627(MiAaPQ)EBC6236142(DE-He213)978-3-030-45193-6(PPN)248598112(EXLCZ)99531000000001662720200623d2020 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierDifferentiable Manifolds[electronic resource] A Theoretical Physics Approach /by Gerardo F. Torres del Castillo2nd ed. 2020.Cham :Springer International Publishing :Imprint: Birkhäuser,2020.1 online resource (447 pages)3-030-45192-5 1 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.This 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.Differential geometryPhysicsTopological groupsLie groupsMechanicsDifferential Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21022Mathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Topological Groups, Lie Groupshttps://scigraph.springernature.com/ontologies/product-market-codes/M11132Classical Mechanicshttps://scigraph.springernature.com/ontologies/product-market-codes/P21018Differential geometry.Physics.Topological groups.Lie groups.Mechanics.Differential Geometry.Mathematical Methods in Physics.Topological Groups, Lie Groups.Classical Mechanics.516.36Torres del Castillo Gerardo Fauthttp://id.loc.gov/vocabulary/relators/aut768202MiAaPQMiAaPQMiAaPQBOOK996418198203316Differentiable Manifolds1936217UNISA