000 03010nam a22005055i 4500
001 978-0-8176-8271-2
003 DE-He213
005 20140220083227.0
007 cr nn 008mamaa
008 111007s2012 xxu| s |||| 0|eng d
020 _a9780817682712
_9978-0-8176-8271-2
024 7 _a10.1007/978-0-8176-8271-2
_2doi
050 4 _aQA613-613.8
050 4 _aQA613.6-613.66
072 7 _aPBMS
_2bicssc
072 7 _aPBPH
_2bicssc
072 7 _aMAT038000
_2bisacsh
082 0 4 _a514.34
_223
100 1 _aTorres del Castillo, Gerardo F.
_eauthor.
245 1 0 _aDifferentiable Manifolds
_h[electronic resource] :
_bA Theoretical Physics Approach /
_cby Gerardo F. Torres del Castillo.
264 1 _aBoston :
_bBirkhäuser Boston,
_c2012.
300 _aVIII, 275p. 20 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPreface.-1 Manifolds.-  2 Lie Derivatives -- 3 Differential Forms -- 4 Integral Manifolds -- 5 Connections -- 6. Riemannian Manifolds -- 7 Lie Groups -- 8 Hamiltonian Classical Mechanics -- References.-Index.
520 _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 work’s 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 (Chapter 4), connections (Chapter 5), Riemannian manifolds (Chapter 6), Lie groups (Chapter 7), and Hamiltonian mechanics (Chapter 8). 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. Differentiable Manifolds is addressed to advanced undergraduate or beginning graduate students in mathematics or physics. Prerequisites include multivariable calculus, linear algebra, differential equations, and (for the last chapter) a basic knowledge of analytical mechanics.
650 0 _aMathematics.
650 0 _aTopological Groups.
650 0 _aCell aggregation
_xMathematics.
650 0 _aMathematical physics.
650 0 _aMechanics.
650 1 4 _aMathematics.
650 2 4 _aManifolds and Cell Complexes (incl. Diff.Topology).
650 2 4 _aMechanics.
650 2 4 _aMathematical Methods in Physics.
650 2 4 _aTopological Groups, Lie Groups.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817682705
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-8176-8271-2
912 _aZDB-2-SMA
999 _c100228
_d100228