Exterior Differential Systems And Euler Lagrange Partial Differential Equations
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Exterior Differential Systems And Euler Lagrange Partial Differential Equations
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Author : Robert Bryant
language : en
Publisher: University of Chicago Press
Release Date : 2003-07
Exterior Differential Systems And Euler Lagrange Partial Differential Equations written by Robert Bryant and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07 with Mathematics categories.
In Exterior Differential Systems, the authors present the results of their ongoing development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincaré-Cartan forms. They also cover certain aspects of the theory of exterior differential systems, which provides the language and techniques for the entire study. Because it plays a central role in uncovering geometric properties of differential equations, the method of equivalence is particularly emphasized. In addition, the authors discuss conformally invariant systems at length, including results on the classification and application of symmetries and conservation laws. The book also covers the Second Variation, Euler-Lagrange PDE systems, and higher-order conservation laws. This timely synthesis of partial differential equations and differential geometry will be of fundamental importance to both students and experienced researchers working in geometric analysis.
Exterior Differential Systems And Euler Lagrange Partial Differential Equations
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Author : Robert Bryant
language : en
Publisher: University of Chicago Press
Release Date : 2003-07-01
Exterior Differential Systems And Euler Lagrange Partial Differential Equations written by Robert Bryant and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-01 with Mathematics categories.
In Exterior Differential Systems, the authors present the results of their ongoing development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincaré-Cartan forms. They also cover certain aspects of the theory of exterior differential systems, which provides the language and techniques for the entire study. Because it plays a central role in uncovering geometric properties of differential equations, the method of equivalence is particularly emphasized. In addition, the authors discuss conformally invariant systems at length, including results on the classification and application of symmetries and conservation laws. The book also covers the Second Variation, Euler-Lagrange PDE systems, and higher-order conservation laws. This timely synthesis of partial differential equations and differential geometry will be of fundamental importance to both students and experienced researchers working in geometric analysis.
Exterior Differential Systems
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Author : Robert L. Bryant
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Exterior Differential Systems written by Robert L. Bryant 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 2013-06-29 with Mathematics categories.
This book gives a treatment of exterior differential systems. It will in clude both the general theory and various applications. An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. When all the forms are linear, it is called a pfaffian system. Our object is to study its integral manifolds, i. e. , submanifolds satisfying all the equations of the system. A fundamental fact is that every equation implies the one obtained by exterior differentiation, so that the complete set of equations associated to an exterior differential system constitutes a differential ideal in the algebra of all smooth forms. Thus the theory is coordinate-free and computations typically have an algebraic character; however, even when coordinates are used in intermediate steps, the use of exterior algebra helps to efficiently guide the computations, and as a consequence the treatment adapts well to geometrical and physical problems. A system of partial differential equations, with any number of inde pendent and dependent variables and involving partial derivatives of any order, can be written as an exterior differential system. In this case we are interested in integral manifolds on which certain coordinates remain independent. The corresponding notion in exterior differential systems is the independence condition: certain pfaffian forms remain linearly indepen dent. Partial differential equations and exterior differential systems with an independence condition are essentially the same object.
Exterior Differential Systems And The Calculus Of Variations
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Author : P.A. Griffiths
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Exterior Differential Systems And The Calculus Of Variations written by P.A. Griffiths 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 2013-06-29 with Mathematics categories.
15 0. PRELIMINARIES a) Notations from Manifold Theory b) The Language of Jet Manifolds c) Frame Manifolds d) Differentia! Ideals e) Exterior Differential Systems EULER-LAGRANGE EQUATIONS FOR DIFFERENTIAL SYSTEMS ~liTH ONE I. 32 INDEPENDENT VARIABLE a) Setting up the Problem; Classical Examples b) Variational Equations for Integral Manifolds of Differential Systems c) Differential Systems in Good Form; the Derived Flag, Cauchy Characteristics, and Prolongation of Exterior Differential Systems d) Derivation of the Euler-Lagrange Equations; Examples e) The Euler-Lagrange Differential System; Non-Degenerate Variational Problems; Examples FIRST INTEGRALS OF THE EULER-LAGRANGE SYSTEM; NOETHER'S II. 1D7 THEOREM AND EXAMPLES a) First Integrals and Noether's Theorem; Some Classical Examples; Variational Problems Algebraically Integrable by Quadratures b) Investigation of the Euler-Lagrange System for Some Differential-Geometric Variational Pro~lems: 2 i) ( K ds for Plane Curves; i i) Affine Arclength; 2 iii) f K ds for Space Curves; and iv) Delauney Problem. II I. EULER EQUATIONS FOR VARIATIONAL PROBLEfiJS IN HOMOGENEOUS SPACES 161 a) Derivation of the Equations: i) Motivation; i i) Review of the Classical Case; iii) the Genera 1 Euler Equations 2 K /2 ds b) Examples: i) the Euler Equations Associated to f for lEn; but for Curves in i i) Some Problems as in i) sn; Non- Curves in iii) Euler Equations Associated to degenerate Ruled Surfaces IV.
Applied Exterior Calculus
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Author : Dominic G. B. Edelen
language : en
Publisher: Courier Corporation
Release Date : 2005-01-01
Applied Exterior Calculus written by Dominic G. B. Edelen and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
This text begins with the essentials, advancing to applications and studies of physical disciplines, including classical and irreversible thermodynamics, electrodynamics, and the theory of gauge fields. Geared toward advanced undergraduates and graduate students, it develops most of the theory and requires only a familiarity with upper-division algebra and mathematical analysis. "Essential." — SciTech Book News. 1985 edition.
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 centres on determining the existence and degree of generality of Lagrangians whose system of Euler-Lagrange equations coicides 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. 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.
Exterior Differential Systems
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Author : Robert L. Bryant
language : en
Publisher:
Release Date : 1991-01
Exterior Differential Systems written by Robert L. Bryant and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01 with Differential equations, Partial categories.
Variational Principles For Second Order Differential Equations Application Of The Spencer Theory Of
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Author : Joseph Grifone
language : en
Publisher: World Scientific
Release Date : 2000-05-25
Variational Principles For Second Order Differential Equations Application Of The Spencer Theory Of 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.
Selected Topics In The Geometrical Study Of Differential Equations
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Author : Niky Kamran
language : en
Publisher: American Mathematical Soc.
Release Date : 2002-01-01
Selected Topics In The Geometrical Study Of Differential Equations written by Niky Kamran 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 2002-01-01 with Mathematics categories.
Differential Systems And Isometric Embeddings
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Author : Phillip A. Griffiths
language : en
Publisher: Princeton University Press
Release Date : 1987-05-21
Differential Systems And Isometric Embeddings written by Phillip A. Griffiths and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-05-21 with Mathematics categories.
The theory of exterior differential systems provides a framework for systematically addressing the typically non-linear, and frequently overdetermined, partial differential equations that arise in differential geometry. Adaptation of the techniques of microlocalization to differential systems have led to recent activity on the foundations of the theory; in particular, the fundamental role of the characteristic variety in geometric problems is now clearly established. In this book the general theory is explained in a relatively quick and concrete manner, and then this general theory is applied to the recent developments in the classical problem of isometric embeddings of Riemannian manifolds.