The Resource Geometric mechanics on Riemannian manifolds : applications to partial differential equations, Ovidiu Calin, DerChen Chang
Geometric mechanics on Riemannian manifolds : applications to partial differential equations, Ovidiu Calin, DerChen Chang
Resource Information
The item Geometric mechanics on Riemannian manifolds : applications to partial differential equations, Ovidiu Calin, DerChen Chang represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Geometric mechanics on Riemannian manifolds : applications to partial differential equations, Ovidiu Calin, DerChen Chang represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 "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. And, conservation laws of the EulerLagrange 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
 Language
 eng
 Extent
 1 online resource (xv, 278 pages).
 Contents

 Introductory Chapter
 Laplace Operators on Riemannian Manifolds
 Lagrangian Formalism on Riemannian Manifolds
 Harmonic Maps from a Lagrangian Viewpoint
 Conservation Theorems
 Hamiltonian Formalism
 HamiltonJacobi Theory
 Minimal Hypersurfaces
 Radially Symmetric Spaces
 Fundamental Solutions for Heat Operators with Potentials
 Fundamental Solutions for Elliptic Operators
 Mechanical Curves
 Isbn
 9780817644215
 Label
 Geometric mechanics on Riemannian manifolds : applications to partial differential equations
 Title
 Geometric mechanics on Riemannian manifolds
 Title remainder
 applications to partial differential equations
 Statement of responsibility
 Ovidiu Calin, DerChen Chang
 Subject

 Differential equations, Partial
 Differential equations, Partial
 Differential equations, Partial
 Global Riemannian geometry
 Global Riemannian geometry
 Global Riemannian geometry
 Géométrie riemannienne globale
 Mechanics, Analytic
 Mechanics, Analytic
 Mechanics, Analytic
 Mécanique analytique
 Partielle Differentialgleichung  Theoretische Mechanik  Riemannsche Geometrie
 Riemann, Variétés de
 Riemannian manifolds
 Riemannian manifolds
 Riemannian manifolds
 Riemannsche Geometrie  Theoretische Mechanik  Partielle Differentialgleichung
 Theoretische Mechanik  Riemannsche Geometrie  Partielle Differentialgleichung
 Équations aux dérivées partielles
 Language
 eng
 Summary
 "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. And, conservation laws of the EulerLagrange 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
 Cataloging source
 COO
 Dewey number
 516.3/73
 Index
 index present
 LC call number
 QA671
 LC item number
 .G46 2005
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName

 Calin, Ovidiu
 Chang, Derchen E
 Series statement
 Applied and Numerical Harmonic Analysis
 http://library.link/vocab/subjectName

 Riemannian manifolds
 Global Riemannian geometry
 Mechanics, Analytic
 Differential equations, Partial
 Riemann, Variétés de
 Géométrie riemannienne globale
 Mécanique analytique
 Équations aux dérivées partielles
 Differential equations, Partial
 Global Riemannian geometry
 Mechanics, Analytic
 Riemannian manifolds
 Riemannsche Geometrie
 Theoretische Mechanik
 Partielle Differentialgleichung
 Label
 Geometric mechanics on Riemannian manifolds : applications to partial differential equations, Ovidiu Calin, DerChen Chang
 Bibliography note
 Includes bibliographical references (pages 271273) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Introductory Chapter  Laplace Operators on Riemannian Manifolds  Lagrangian Formalism on Riemannian Manifolds  Harmonic Maps from a Lagrangian Viewpoint  Conservation Theorems  Hamiltonian Formalism  HamiltonJacobi Theory  Minimal Hypersurfaces  Radially Symmetric Spaces  Fundamental Solutions for Heat Operators with Potentials  Fundamental Solutions for Elliptic Operators  Mechanical Curves
 Control code
 619481767
 Dimensions
 unknown
 Extent
 1 online resource (xv, 278 pages).
 Form of item
 online
 Isbn
 9780817644215
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/b138771
 http://library.link/vocab/ext/overdrive/overdriveId
 133575
 Specific material designation
 remote
 System control number
 (OCoLC)619481767
 Label
 Geometric mechanics on Riemannian manifolds : applications to partial differential equations, Ovidiu Calin, DerChen Chang
 Bibliography note
 Includes bibliographical references (pages 271273) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Introductory Chapter  Laplace Operators on Riemannian Manifolds  Lagrangian Formalism on Riemannian Manifolds  Harmonic Maps from a Lagrangian Viewpoint  Conservation Theorems  Hamiltonian Formalism  HamiltonJacobi Theory  Minimal Hypersurfaces  Radially Symmetric Spaces  Fundamental Solutions for Heat Operators with Potentials  Fundamental Solutions for Elliptic Operators  Mechanical Curves
 Control code
 619481767
 Dimensions
 unknown
 Extent
 1 online resource (xv, 278 pages).
 Form of item
 online
 Isbn
 9780817644215
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/b138771
 http://library.link/vocab/ext/overdrive/overdriveId
 133575
 Specific material designation
 remote
 System control number
 (OCoLC)619481767
Subject
 Differential equations, Partial
 Differential equations, Partial
 Differential equations, Partial
 Global Riemannian geometry
 Global Riemannian geometry
 Global Riemannian geometry
 Géométrie riemannienne globale
 Mechanics, Analytic
 Mechanics, Analytic
 Mechanics, Analytic
 Mécanique analytique
 Partielle Differentialgleichung  Theoretische Mechanik  Riemannsche Geometrie
 Riemann, Variétés de
 Riemannian manifolds
 Riemannian manifolds
 Riemannian manifolds
 Riemannsche Geometrie  Theoretische Mechanik  Partielle Differentialgleichung
 Theoretische Mechanik  Riemannsche Geometrie  Partielle Differentialgleichung
 Équations aux dérivées partielles
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/GeometricmechanicsonRiemannianmanifolds/JIZe6yw0ZVQ/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/GeometricmechanicsonRiemannianmanifolds/JIZe6yw0ZVQ/">Geometric mechanics on Riemannian manifolds : applications to partial differential equations, Ovidiu Calin, DerChen Chang</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>