000 | 04031nam a22005775i 4500 | ||
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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 |
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337 |
_acomputer _bc _2rdamedia |
||
338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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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 |