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" Geometric mechanics on Riemannian manifolds : "
Ovidiu Calin, Der-Chen Chang
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BL
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| Record Number
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700598
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| Doc. No
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b522787
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| Title & Author
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Geometric mechanics on Riemannian manifolds : : applications to partial differential equations /\ Ovidiu Calin, Der-Chen Chang
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| Publication Statement
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Boston :: Birkhäuser,, [2005]
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, ©2005
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| Series Statement
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Applied and numerical harmonic analysis
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| Page. NO
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xv, 278 pages ;; 24 cm
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| ISBN
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0817643540
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: 9780817643546
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| Bibliographies/Indexes
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Includes bibliographical references (pages 271-273) and index
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| Abstract
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"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 Schrodinger'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
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And, conservation laws of the Euler-Lagrange equations are employed to solve the equations of motion qualitatively when quantitative analysis is not possible." "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."--Jacket
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| Subject
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Differential equations, Partial
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Global Riemannian geometry
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Mechanics, Analytic
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Riemannian manifolds
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| Dewey Classification
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516.3/73
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| LC Classification
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QA671.G46 2005
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| Added Entry
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Calin, Ovidiu
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Chang, Der-chen E
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