Exterior Differential Systems And Equivalence Problems
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Exterior Differential Systems And Equivalence Problems
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Author : Kichoon Yang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Exterior Differential Systems And Equivalence Problems written by Kichoon Yang 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 2013-03-14 with Mathematics categories.
This monograph presents a concise yet elementary account of exterior differential system theory so that it can be quickly applied to problems. The first part of the monograph, Chapters 1-5, deals with the general theory: the Cartan-Kaehler theorem is proved, the notions of involution and prolongation are carefully laid out, quasi-linear differential systems are examined in detail, and explicit examples of the Spencer cohomology groups and the characteristic variety are given. The second part of the monograph, Chapters 6 and 7, deals with applications to problems in differential geometry: the isometric embedding theorem of Cartan-Janet and its various geometric ramifications are discussed, a proof of the Andreotti-Hill theorem on the O-R embedding problem is given, and embeddings of abstract projective structures are discussed. For researchers and graduate students who would like a good introduction to exterior differential systems. This volume will also be particularly useful to those whose work involves differential geometry and partial differential equations.
Exterior Differential Systems And Equivalence Problems
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Author : Kichoon Yang
language : en
Publisher:
Release Date : 2014-01-15
Exterior Differential Systems And Equivalence Problems written by Kichoon Yang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
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 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 Nonholonomic Motion Planning
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Author : Dawn Marie Tilbury
language : en
Publisher:
Release Date : 1994
Exterior Differential Systems And Nonholonomic Motion Planning written by Dawn Marie Tilbury and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with 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.
Using The Mathematics Literature
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Author : Kristine K. Fowler
language : en
Publisher: CRC Press
Release Date : 2004-05-25
Using The Mathematics Literature written by Kristine K. Fowler and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-25 with Language Arts & Disciplines categories.
This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathemati
Topics In The Geometric Theory Of Linear Systems
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Author : Robert Hermann
language : en
Publisher:
Release Date : 1984
Topics In The Geometric Theory Of Linear Systems written by Robert Hermann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Differential Algebra And Related Topics
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Author : Li Guo
language : en
Publisher: World Scientific
Release Date : 2002
Differential Algebra And Related Topics written by Li Guo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Differential algebra explores properties of solutions of systems of (ordinary or partial, linear or non-linear) differential equations from an algebraic point of view. It includes as special cases algebraic systems as well as differential systems with algebraic constraints. This algebraic theory of Joseph F Ritt and Ellis R Kolchin is further enriched by its interactions with algebraic geometry, Diophantine geometry, differential geometry, model theory, control theory, automatic theorem proving, combinatorics, and difference equations. Differential algebra now plays an important role in computational methods such as symbolic integration and symmetry analysis of differential equations. These proceedings consist of tutorial and survey papers presented at the Second International Workshop on Differential Algebra and Related Topics at Rutgers University, Newark in April 2007. As a sequel to the proceedings of the First International Workshop, this volume covers more related subjects, and provides a modern and introductory treatment to many facets of differential algebra, including surveys of known results, open problems, and new, emerging, directions of research. It is therefore an excellent companion and reference text for graduate students and researchers.
Differential Geometry Global Analysis And Topology
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Author : Canadian Mathematical Society. Summer Meeting
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Differential Geometry Global Analysis And Topology written by Canadian Mathematical Society. Summer Meeting 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 book contains the proceedings of a special session on differential geometry, global analysis, and topology, held during the Summer Meeting of the Canadian Mathematical Society in June 1990 at Dalhousie University in Halifax. The session featured many fascinating talks on topics of current interest. The articles collected here reflect the diverse interests of the participants but are united by the common theme of the interplay among geometry, global analysis, and topology. Some of the topics include applications to low dimensional manifolds, control theory, integrable systems, Lie algebras of operators, and algebraic geometry. Readers will appreciate the insight the book provides into some recent trends in these areas.