Calculus With Differential Equations Bundle
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Calculus With Differential Equations Bundle
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Author : Ross Finney
language : en
Publisher: Addison-Wesley Longman
Release Date : 1994-01
Calculus With Differential Equations Bundle written by Ross Finney and has been published by Addison-Wesley Longman this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01 with categories.
Vector Bundles And Differential Equations
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Author : André Hirschowitz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Vector Bundles And Differential Equations written by André Hirschowitz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Geometric Approaches To Differential Equations
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Author : Peter J. Vassiliou
language : en
Publisher: Cambridge University Press
Release Date : 2000-03-13
Geometric Approaches To Differential Equations written by Peter J. Vassiliou and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-13 with Mathematics categories.
A concise and accessible introduction to the wide range of topics in geometric approaches to differential equations.
Introduction To Differential Geometry With Applications To Navier Stokes Dynamics
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Author : Troy L Story
language : en
Publisher: iUniverse
Release Date : 2005
Introduction To Differential Geometry With Applications To Navier Stokes Dynamics written by Troy L Story and has been published by iUniverse this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Geometry, Differential categories.
Introduction to Differential Geometry with applications to Navier-Stokes Dynamics is an invaluable manuscript for anyone who wants to understand and use exterior calculus and differential geometry, the modern approach to calculus and geometry. Author Troy Story makes use of over thirty years of research experience to provide a smooth transition from conventional calculus to exterior calculus and differential geometry, assuming only a knowledge of conventional calculus. Introduction to Differential Geometry with applications to Navier-Stokes Dynamics includes the topics: Geometry, Exterior calculus, Homology and co-homology, Applications of differential geometry and exterior calculus to: Hamiltonian mechanics, geometric optics, irreversible thermodynamics, black hole dynamics, electromagnetism, classical string fields, and Navier-Stokes dynamics.
The Geometry Of Jet Bundles
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Author : D. J. Saunders
language : en
Publisher: Cambridge University Press
Release Date : 1989-03-09
The Geometry Of Jet Bundles written by D. J. Saunders and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-03-09 with Mathematics categories.
The purpose of this book is to , particularly those associated with the calculus of variations, in a modern geometric way.
Variational Principles For Second Order Differential Equations
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Author : Joseph Grifone
language : en
Publisher: World Scientific
Release Date : 2000-05-25
Variational Principles For Second Order Differential Equations written by Joseph Grifone and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-25 with Mathematics categories.
The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations. This book looks at second-order differential equations and asks if they can be written as Euler–Lagrangian equations. If the equations are quadratic, the problem reduces to the characterization of the connections which are Levi–Civita for some Riemann metric. To solve the inverse problem, the authors use the formal integrability theory of overdetermined partial differential systems in the Spencer–Quillen–Goldschmidt version. The main theorems of the book furnish a complete illustration of these techniques because all possible situations appear: involutivity, 2-acyclicity, prolongation, computation of Spencer cohomology, computation of the torsion, etc. Contents:An Introduction to Formal Integrability Theory of Partial Differential SystemsFrölicher–Nijenhuis Theory of DerivationsDifferential Algebraic Formalism of ConnectionsNecessary Conditions for Variational SpraysObstructions to the Integrability of the Euler–Lagrange SystemThe Classification of Locally Variational Sprays on Two-Dimensional ManifoldsEuler–Lagrange Systems in the Isotropic Case Readership: Mathematicians. Keywords:Calculus of Variations;Inverse Problem;Euler-Lagrange Equation;Sprays;Formal Integrability;Involution;Janet-Riquier Theory;Spencer TheoryReviews: “Everybody seriously interested in the modern theory of the inverse problem of the calculus of variations should take a look at this book.” Zentralblatt MATH
Partial Differential Equations
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Author : Donald Clayton Spencer
language : en
Publisher: American Mathematical Soc.
Release Date : 1973
Partial Differential Equations written by Donald Clayton Spencer and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Mathematics categories.
Cohomological Analysis Of Partial Differential Equations And Secondary Calculus
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Author : A. M. Vinogradov
language : en
Publisher: American Mathematical Soc.
Release Date : 2001-10-16
Cohomological Analysis Of Partial Differential Equations And Secondary Calculus written by A. M. Vinogradov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-10-16 with Mathematics categories.
This book is dedicated to fundamentals of a new theory, which is an analog of affine algebraic geometry for (nonlinear) partial differential equations. This theory grew up from the classical geometry of PDE's originated by S. Lie and his followers by incorporating some nonclassical ideas from the theory of integrable systems, the formal theory of PDE's in its modern cohomological form given by D. Spencer and H. Goldschmidt and differential calculus over commutative algebras (Primary Calculus). The main result of this synthesis is Secondary Calculus on diffieties, new geometrical objects which are analogs of algebraic varieties in the context of (nonlinear) PDE's. Secondary Calculus surprisingly reveals a deep cohomological nature of the general theory of PDE's and indicates new directions of its further progress. Recent developments in quantum field theory showed Secondary Calculus to be its natural language, promising a nonperturbative formulation of the theory. In addition to PDE's themselves, the author describes existing and potential applications of Secondary Calculus ranging from algebraic geometry to field theory, classical and quantum, including areas such as characteristic classes, differential invariants, theory of geometric structures, variational calculus, control theory, etc. This book, focused mainly on theoretical aspects, forms a natural dipole with Symmetries and Conservation Laws for Differential Equations of Mathematical Physics, Volume 182 in this same series, Translations of Mathematical Monographs, and shows the theory "in action".
Differential Equations On Manifolds And Mathematical Physics
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Author : Vladimir M. Manuilov
language : en
Publisher: Springer Nature
Release Date : 2022-01-21
Differential Equations On Manifolds And Mathematical Physics written by Vladimir M. Manuilov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-21 with Mathematics categories.
This is a volume originating from the Conference on Partial Differential Equations and Applications, which was held in Moscow in November 2018 in memory of professor Boris Sternin and attracted more than a hundred participants from eighteen countries. The conference was mainly dedicated to partial differential equations on manifolds and their applications in mathematical physics, geometry, topology, and complex analysis. The volume contains selected contributions by leading experts in these fields and presents the current state of the art in several areas of PDE. It will be of interest to researchers and graduate students specializing in partial differential equations, mathematical physics, topology, geometry, and their applications. The readers will benefit from the interplay between these various areas of mathematics.
The Inverse Problem Of The Calculus Of Variations For Ordinary Differential Equations
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Author : Ian Anderson
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
The Inverse Problem Of The Calculus Of Variations For Ordinary Differential Equations written by Ian Anderson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
This monograph explores various aspects of the inverse problem of the calculus of variations for systems of ordinary differential equations. The main problem centers on determining the existence and degree of generality of Lagrangians whose system of Euler-Lagrange equations coincides with a given system of ordinary differential equations. The authors rederive the basic necessary and sufficient conditions of Douglas for second order equations and extend them to equations of higher order using methods of the variational bicomplex of Tulcyjew, Vinogradov, and Tsujishita. What emerges is a fundamental dichotomy between second and higher order systems: the most general Lagrangian for any higher order system can depend only upon finitely many constants. The authors present an algorithm, based upon exterior differential systems techniques, for solving the inverse problem for second order equations. A number of new examples illustrate the effectiveness of this approach. The monograph also contains a study of the inverse problem for a pair of geodesic equations arising from a two dimensional symmetric affine connection. The various possible solutions to the inverse problem for these equations are distinguished by geometric properties of the Ricci tensor.