000 04043nam a22005415i 4500
003 DE-He213
005 20191011023553.0
007 cr nn 008mamaa
008 100301s2005 xxu| s |||| 0|eng d
020 6 4 _a9780817644215
_9978-0-8176-4421-5
024 8 7 _a10.1007/b138771
_2doi
050 8 4 _aQA641-670
072 8 7 _aPBMP
_2bicssc
072 8 7 _aMAT012030
_2bisacsh
082 _a516.36
_223
100 8 1 _aCalin, Ovidiu.
_eauthor.
_931908
245 9 7 _aGeometric Mechanics on Riemannian Manifolds
_h[electronic resource] :
_bApplications to Partial Differential Equations /
_cby Ovidiu Calin, Der-Chen Chang.
001 000047712
300 6 4 _aXVI, 278 p. 26 illus.
_bonline resource.
490 8 1 _aApplied and Numerical Harmonic Analysis
505 8 0 _aIntroductory Chapter -- Laplace Operators on Riemannian Manifolds -- Lagrangian Formalism on Riemannian Manifolds -- Harmonic Maps from a Lagrangian Viewpoint -- Conservation Theorems -- Hamiltonian Formalism -- Hamilton-Jacobi Theory -- Minimal Hypersurfaces -- Radially Symmetric Spaces -- Fundamental Solutions for Heat Operators with Potentials -- Fundamental Solutions for Elliptic Operators -- Mechanical Curves.
520 6 4 _aDifferential geometry techniques have very useful and important applications in partial differential equations and quantum mechanics. This work presents a purely geometric treatment of problems in physics involving quantum harmonic oscillators, quartic oscillators, minimal surfaces, and Schrȵdinger's, Einstein's and Newton's equations. Historically, problems in these areas were approached using the Fourier transform or path integrals, although in some cases (e.g., the case of quartic oscillators) these methods do not work. New geometric methods are introduced in the work that have the advantage of providing quantitative or at least qualitative descriptions of operators, many of which cannot be treated by other methods. And, conservation laws of the EulerLagrange equations are employed to solve the equations of motion qualitatively when quantitative analysis is not possible. Main topics include: Lagrangian formalism on Riemannian manifolds; energy momentum tensor and conservation laws; Hamiltonian formalism; HamiltonJacobi theory; harmonic functions, maps, and geodesics; fundamental solutions for heat operators with potential; and a variational approach to mechanical curves. The text is enriched with good examples and exercises at the end of every chapter. Geometric Mechanics on Riemannian Manifolds is a fine text for a course or seminar directed at graduate and advanced undergraduate students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics. It is also an ideal resource for pure and applied mathematicians and theoretical physicists working in these areas.
650 8 0 _aMathematics.
_98571
650 8 0 _aHarmonic analysis.
_931909
650 8 0 _aDifferential equations, partial.
_99614
650 8 0 _aGlobal differential geometry.
_99530
650 8 0 _aMathematical physics.
_99251
650 _aMathematics.
_98571
650 _aDifferential Geometry.
_99532
650 _aPartial Differential Equations.
_99616
650 _aMathematical Methods in Physics.
_99252
650 _aAbstract Harmonic Analysis.
_931910
650 _aApplications of Mathematics.
_99618
700 8 1 _aChang, Der-Chen.
_eauthor.
_931911
710 8 2 _aSpringerLink (Online service)
_931912
773 8 0 _tSpringer eBooks
776 _iPrinted edition:
_z9780817643546
830 8 0 _aApplied and Numerical Harmonic Analysis
_931913
856 _uhttp://dx.doi.org/10.1007/b138771
_zde clik aquí para ver el libro electrónico
264 8 1 _aBoston, MA :
_bBirkhuser Boston,
_c2005.
336 6 4 _atext
_btxt
_2rdacontent
337 6 4 _acomputer
_bc
_2rdamedia
338 6 4 _aonline resource
_bcr
_2rdacarrier
347 6 4 _atext file
_bPDF
_2rda
516 6 4 _aZDB-2-SMA
999 _c47441
_d47441
942 _c05