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Partial Differential Equations and Group Theory: New Perspectives for Applications (Mathematics and Its Applications) - Softcover
Synopsis
Ordinary differential control thPory (the classical theory) studies input/output re lations defined by systems of ordinary differential equations (ODE). The various con cepts that can be introduced (controllability, observability, invertibility, etc. ) must be tested on formal objects (matrices, vector fields, etc. ) by means of formal operations (multiplication, bracket, rank, etc. ), but without appealing to the explicit integration (search for trajectories, etc. ) of the given ODE. Many partial results have been re cently unified by means of new formal methods coming from differential geometry and differential algebra. However, certain problems (invariance, equivalence, linearization, etc. ) naturally lead to systems of partial differential equations (PDE). More generally, partial differential control theory studies input/output relations defined by systems of PDE (mechanics, thermodynamics, hydrodynamics, plasma physics, robotics, etc. ). One of the aims of this book is to extend the preceding con cepts to this new situation, where, of course, functional analysis and/or a dynamical system approach cannot be used. A link will be exhibited between this domain of applied mathematics and the famous 'Backlund problem', existing in the study of solitary waves or solitons. In particular, we shall show how the methods of differ ential elimination presented here will allow us to determine compatibility conditions on input and/or output as a better understanding of the foundations of control the ory. At the same time we shall unify differential geometry and differential algebra in a new framework, called differential algebraic geometry.
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Partial Differential Equations and Group Theory : New Perspectives for Applications
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Partial Differential Equations and Group Theory: New Perspectives for Applications (Mathematics and Its Applications)
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Partial Differential Equations and Group Theory (Paperback)
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Springer, Dordrecht, 2010
ISBN 10: 9048144329
ISBN 13: 9789048144327
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Paperback. Condition: new. Paperback. The formal theory of systems of partial differential equations (PDEs) was developed by D.C. Spencer in the U.S.A. during 1960--1975; it studies the solution spaces of systems of PDEs without especially integrating them. It also allows the study of Lie pseudogroups, i.e. groups of transformation solutions of systems of PDEs. Although this work supersedes the classical approaches of M. Janet and E. Cartan, it is still largely unknown by mathematicians and has never been used by physicists. This book provides a self-contained introduction to these methods, with illustrations and specific examples coming from many branches of physics, the engineering sciences and applied mathematics. The algorithms involved are presented in a way that allows the use of computer algebra for the intrinsic study of nonlinear PDEs. The book also for the first time presents the group-theoretical unification of the finite element methods for elasticity, heat and electromagnetism. The book contains the material of an intensive course which has been given many times with much success throughout Europe, and can be used for a one-year course at graduate level.For researchers in mathematics, mathematical physics, computer algebra, control theory and theoretical mechanics. Ordinary differential control thPory (the classical theory) studies input/output re lations defined by systems of ordinary differential equations (ODE). At the same time we shall unify differential geometry and differential algebra in a new framework, called differential algebraic geometry. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9789048144327
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Partial Differential Equations and Group Theory: New Perspectives for Applications (Mathematics and Its Applications)
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Partial Differential Equations and Group Theory : New Perspectives for Applications
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Partial Differential Equations and Group Theory: New Perspectives for Applications (Mathematics and Its Applications)
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Partial Differential Equations and Group Theory: New Perspectives for Applications (Mathematics and Its Applications)
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Partial Differential Equations and Group Theory
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Springer Netherlands Dez 2010, 2010
ISBN 10: 9048144329
ISBN 13: 9789048144327
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Ordinary differential control thPory (the classical theory) studies input/output re lations defined by systems of ordinary differential equations (ODE). The various con cepts that can be introduced (controllability, observability, invertibility, etc. ) must be tested on formal objects (matrices, vector fields, etc. ) by means of formal operations (multiplication, bracket, rank, etc. ), but without appealing to the explicit integration (search for trajectories, etc. ) of the given ODE. Many partial results have been re cently unified by means of new formal methods coming from differential geometry and differential algebra. However, certain problems (invariance, equivalence, linearization, etc. ) naturally lead to systems of partial differential equations (PDE). More generally, partial differential control theory studies input/output relations defined by systems of PDE (mechanics, thermodynamics, hydrodynamics, plasma physics, robotics, etc. ). One of the aims of this book is to extend the preceding con cepts to this new situation, where, of course, functional analysis and/or a dynamical system approach cannot be used. A link will be exhibited between this domain of applied mathematics and the famous 'Backlund problem', existing in the study of solitary waves or solitons. In particular, we shall show how the methods of differ ential elimination presented here will allow us to determine compatibility conditions on input and/or output as a better understanding of the foundations of control the ory. At the same time we shall unify differential geometry and differential algebra in a new framework, called differential algebraic geometry. 492 pp. Englisch. Seller Inventory # 9789048144327
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Partial Differential Equations and Group Theory
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Partial Differential Equations and Group Theory
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Condition: New. Print on Demand pp. 488 49:B&W 6.14 x 9.21 in or 234 x 156 mm (Royal 8vo) Perfect Bound on White w/Gloss Lam. Seller Inventory # 5825865
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