000 04031nam a22005775i 4500
001 978-0-8176-4421-5
003 DE-He213
005 20161121230927.0
007 cr nn 008mamaa
008 100301s2005 xxu| s |||| 0|eng d
020 _a9780817644215
_9978-0-8176-4421-5
024 7 _a10.1007/b138771
_2doi
050 4 _aQA403.5-404.5
072 7 _aPBKF
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515.2433
_223
100 1 _aCalin, Ovidiu.
_eauthor.
245 1 0 _aGeometric Mechanics on Riemannian Manifolds
_h[electronic resource] :
_bApplications to Partial Differential Equations /
_cby Ovidiu Calin, Der-Chen Chang.
264 1 _aBoston, MA :
_bBirkhäuser Boston,
_c2005.
300 _aXVI, 278 p. 26 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aApplied and Numerical Harmonic Analysis
505 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 _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.
650 0 _aMathematics.
650 0 _aHarmonic analysis.
650 0 _aFourier analysis.
650 0 _aPartial differential equations.
650 0 _aApplied mathematics.
650 0 _aEngineering mathematics.
650 0 _aDifferential geometry.
650 0 _aPhysics.
650 1 4 _aMathematics.
650 2 4 _aFourier Analysis.
650 2 4 _aDifferential Geometry.
650 2 4 _aPartial Differential Equations.
650 2 4 _aMathematical Methods in Physics.
650 2 4 _aAbstract Harmonic Analysis.
650 2 4 _aApplications of Mathematics.
700 1 _aChang, Der-Chen.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817643546
830 0 _aApplied and Numerical Harmonic Analysis
856 4 0 _uhttp://dx.doi.org/10.1007/b138771
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c506042
_d506042