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024 7 $a10.1007/978-94-007-5345-7
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035   $a(OCoLC)820879071
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035   $a(DE-He213)978-94-007-5345-7
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035   $a(PPN)16834064X
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100   $a20121116d2013      u|             0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aDifferential Geometry and Mathematical Physics$b[electronic resource] $ePart I. Manifolds, Lie Groups and Hamiltonian Systems /$fby Gerd Rudolph, Matthias Schmidt
205   $a1st ed. 2013.
210  1$aDordrecht :$cSpringer Netherlands :$cImprint: Springer,$d2013.
215   $a1 online resource (765 p.)
225 1 $aTheoretical and Mathematical Physics,$x1864-5879
300   $aDescription based upon print version of record.
311   $a94-017-8198-2 
311   $a94-007-5344-6 
320   $aIncludes bibliographical references and index.
327   $a1 Differentiable manifolds --  2 Vector bundles --  3 Vector fields --  4 Differential forms --  5 Lie groups --  6 Lie group actions --  7 Linear symplectic algebra --  8 Symplectic geometry --  9 Hamiltonian systems --  10 Symmetries -- 11 Integrability -- 12 Hamilton-Jacobi theory --  References.
330   $aStarting from an undergraduate level, this book systematically develops the basics of ? Calculus on manifolds, vector bundles, vector fields and differential forms, ? Lie groups and Lie group actions, ? Linear symplectic algebra and symplectic geometry, ? Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.
410  0$aTheoretical and Mathematical Physics,$x1864-5879
606   $aPhysics
606   $aGlobal analysis (Mathematics)
606   $aManifolds (Mathematics)
606   $aMechanics
606   $aTopological groups
606   $aLie groups
606   $aDifferential geometry
606   $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013
606   $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082
606   $aClassical Mechanics$3https://scigraph.springernature.com/ontologies/product-market-codes/P21018
606   $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132
606   $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022
615  0$aPhysics.
615  0$aGlobal analysis (Mathematics).
615  0$aManifolds (Mathematics).
615  0$aMechanics.
615  0$aTopological groups.
615  0$aLie groups.
615  0$aDifferential geometry.
615 14$aMathematical Methods in Physics.
615 24$aGlobal Analysis and Analysis on Manifolds.
615 24$aClassical Mechanics.
615 24$aTopological Groups, Lie Groups.
615 24$aDifferential Geometry.
676   $a515.7
676   $a516.36
700   $aRudolph$b Gerd$4aut$4http://id.loc.gov/vocabulary/relators/aut$0764074
702   $aSchmidt$b Matthias$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910736987103321
996   $aDifferential geometry and mathematical physics$91550986
997   $aUNINA