Klik op een omslag om naar Google Boeken te gaan.
Bezig met laden... Geometric Mechanics on Riemannian Manifolds: Applications to Partial Differential Equations (Applied and Numerical Harmonic Analysis)door Ovidiu Calin
Geen Bezig met laden...
Meld je aan bij LibraryThing om erachter te komen of je dit boek goed zult vinden. Op dit moment geen Discussie gesprekken over dit boek. Geen besprekingen geen besprekingen | voeg een bespreking toe
Onderdeel van de reeks(en)
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. Geen bibliotheekbeschrijvingen gevonden. |
Actuele discussiesGeen
Google Books — Bezig met laden... GenresDewey Decimale Classificatie (DDC)516.3Natural sciences and mathematics Mathematics Geometry Analytic GeometryLC-classificatieWaarderingGemiddelde: Geen beoordelingen.Ben jij dit?Word een LibraryThing Auteur. |