Geometric mechanics on Riemannian manifolds : applications to partial differential equations
Differential 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&...
में बचाया:
| मुख्य लेखकों: | , |
|---|---|
| स्वरूप: | Livre numérique |
| भाषा: | Anglais |
| प्रकाशित: |
Boston, MA :
Birkhäuser Boston
[20..].
Cham : Springer Nature |
| संस्करण: | 1st ed. 2005. |
| श्रृंखला: | Applied and Numerical Harmonic Analysis
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| विषय: | |
| ऑनलाइन पहुंच: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| टिप्पणी: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Geometric mechanics on Riemannian manifolds, applications to partial differential equations, Ovidiu Calin, Der-Chen Chang, 2005, Boston, Birkhäuser, 1 vol. (XV-278 p.), Applied and numerical harmonic analysis, 0-8176-4354-0 • Geometric Mechanics on Riemannian Manifolds, Texte imprimé, 9780817670764 |
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| 100 | 1 | |a Calin, Ovidiu, |d 19..-...., |c Mathématicien. | |
| 245 | 1 | 0 | |a Geometric mechanics on Riemannian manifolds : |b applications to partial differential equations |c by Ovidiu Calin, Der-Chen Chang. |
| 250 | |a 1st ed. 2005. | ||
| 260 | |a Boston, MA : |b Birkhäuser Boston. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Applied and Numerical Harmonic Analysis |x 2296-5017 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 1 | |a Introductory 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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a Differential 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 | |a Riemann, Variétés de | ||
| 650 | |a Géométrie riemannienne globale | ||
| 650 | |a Mécanique analytique | ||
| 650 | |a Équations aux dérivées partielles | ||
| 700 | 1 | |a Chang, Der-Chen Edward, |d 19..- |4 aut | |
| 776 | 0 | |0 094347131 |t Geometric mechanics on Riemannian manifolds |o applications to partial differential equations |f Ovidiu Calin, Der-Chen Chang |d 2005 |c Boston |n Birkhäuser |p 1 vol. (XV-278 p.) |s Applied and numerical harmonic analysis |z 0-8176-4354-0 | |
| 776 | 0 | |t Geometric Mechanics on Riemannian Manifolds |b Texte imprimé |z 9780817670764 | |
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| 856 | 4 | |5 452349901:748048006 |u https://ezproxy.univ-orleans.fr/login?url=https://dx.doi.org/10.1007/b138771 |z Accès Université d'Orléans | |
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