03745nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020001800100020001900118024002500137082001500162100002800177245015700205264004600362300003300408336002600441337002600467338003600493347002400529490004400553505042300597520168101020650001702701650002302718650003702741650003402778650002602812650001702838650002702855650003602882650003702918650003202955650003302987700003003020710003403050773002003084776003603104830004403140856009103184978-0-8176-4421-5DE-He21320260521092025.0cr nn 008mamaa100301s2005    xxu|    s    |||| 0|eng d  a9780817644215  a997808176442157 a10.1007/b1387712doi04a516.362231 aCalin, Ovidiu.eauthor.10aGeometric Mechanics on Riemannian Manifoldsh[electronic resource] :bApplications to Partial Differential Equations /cby Ovidiu Calin, Der-Chen Chang. 1aBoston, MA :bBirkhäuser Boston,c2005.  aXV, 278 p.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aApplied and Numerical Harmonic Analysis0 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.  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 Schrödinger'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 Euler-Lagrange 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; Hamilton-Jacobi 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. 0aMATHEMATICS. 0aHARMONIC ANALYSIS. 0aDIFFERENTIAL EQUATIONS, PARTIAL. 0aGLOBAL DIFFERENTIAL GEOMETRY. 0aMATHEMATICAL PHYSICS.14aMATHEMATICS.24aDIFFERENTIAL GEOMETRY.24aPARTIAL DIFFERENTIAL EQUATIONS.24aMATHEMATICAL METHODS IN PHYSICS.24aABSTRACT HARMONIC ANALYSIS.24aAPPLICATIONS OF MATHEMATICS.1 aChang, Der-Chen.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780817643546 0aApplied and Numerical Harmonic Analysis40uhttp://dx.doi.org/10.1007/b138771zVer el texto completo en las instalaciones del CICY