Geometric And Algebraic Structures In Differential Equations
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Geometric And Algebraic Structures In Differential Equations
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Author : P.H. Kersten
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric And Algebraic Structures In Differential Equations written by P.H. Kersten 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.
The geometrical theory of nonlinear differential equations originates from classical works by S. Lie and A. Bäcklund. It obtained a new impulse in the sixties when the complete integrability of the Korteweg-de Vries equation was found and it became clear that some basic and quite general geometrical and algebraic structures govern this property of integrability. Nowadays the geometrical and algebraic approach to partial differential equations constitutes a special branch of modern mathematics. In 1993, a workshop on algebra and geometry of differential equations took place at the University of Twente (The Netherlands), where the state-of-the-art of the main problems was fixed. This book contains a collection of invited lectures presented at this workshop. The material presented is of interest to those who work in pure and applied mathematics and especially in mathematical physics.
Geometric And Algebraic Structures In Differential Equations
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Author : I. S Krasil'shchik
language : en
Publisher:
Release Date : 1995
Geometric And Algebraic Structures In Differential Equations written by I. S Krasil'shchik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
Differential Geometric Structures
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Author : Walter A. Poor
language : en
Publisher: Courier Corporation
Release Date : 2015-04-27
Differential Geometric Structures written by Walter A. Poor and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-27 with Mathematics categories.
This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.
Clifford Algebra To Geometric Calculus
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Author : David Hestenes
language : en
Publisher: Springer Science & Business Media
Release Date : 1984
Clifford Algebra To Geometric Calculus written by David Hestenes 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 1984 with Mathematics categories.
Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebra' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quaternions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.
Metric Structures In Differential Geometry
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Author : Gerard Walschap
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-03-18
Metric Structures In Differential Geometry written by Gerard Walschap 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 2004-03-18 with Mathematics categories.
This book offers an introduction to the theory of differentiable manifolds and fiber bundles. It examines bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle. These concepts are illustrated in detail for bundles over spheres.
Analytic Algebraic And Geometric Aspects Of Differential Equations
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Author : Galina Filipuk
language : en
Publisher: Birkhäuser
Release Date : 2017-06-23
Analytic Algebraic And Geometric Aspects Of Differential Equations written by Galina Filipuk and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-23 with Mathematics categories.
This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of interest to graduate students, early-career researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques.
Difference Algebra
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Author : Alexander Levin
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-19
Difference Algebra written by Alexander Levin 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 2008-04-19 with Mathematics categories.
Difference algebra grew out of the study of algebraic difference equations with coefficients from functional fields. The first stage of this development of the theory is associated with its founder, J.F. Ritt (1893-1951), and R. Cohn, whose book Difference Algebra (1965) remained the only fundamental monograph on the subject for many years. Nowadays, difference algebra has overgrown the frame of the theory of ordinary algebraic difference equations and appears as a rich theory with applications to the study of equations in finite differences, functional equations, differential equations with delay, algebraic structures with operators, group and semigroup rings. The monograph is intended for graduate students and researchers in difference and differential algebra, commutative algebra, ring theory, and algebraic geometry. The book is self-contained; it requires no prerequisites other than the knowledge of basic algebraic concepts and a mathematical maturity of an advanced undergraduate.
Geometry In Partial Differential Equations
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Author : Agostino Prastaro
language : en
Publisher: World Scientific
Release Date : 1994
Geometry In Partial Differential Equations written by Agostino Prastaro and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
This book emphasizes the interdisciplinary interaction in problems involving geometry and partial differential equations. It provides an attempt to follow certain threads that interconnect various approaches in the geometric applications and influence of partial differential equations. A few such approaches include: Morse-Palais-Smale theory in global variational calculus, general methods to obtain conservation laws for PDEs, structural investigation for the understanding of the meaning of quantum geometry in PDEs, extensions to super PDEs (formulated in the category of supermanifolds) of the geometrical methods just introduced for PDEs and the harmonic theory which proved to be very important especially after the appearance of the Atiyah-Singer index theorem, which provides a link between geometry and topology.
Special Issue On Geometric And Algebraic Structures In Differential Equations
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Author : Paul H. M. Kersten
language : en
Publisher:
Release Date : 1995
Special Issue On Geometric And Algebraic Structures In Differential Equations written by Paul H. M. Kersten and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
The Interplay Between Differential Geometry And Differential Equations
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Author : Valentin Vasilʹevich Lychagin
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
The Interplay Between Differential Geometry And Differential Equations written by Valentin Vasilʹevich Lychagin 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 1995 with Differential equations, Nonlinear categories.