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ISBN: 0387909206 0387961720 1461211328 9780387909202 Year: 1984 Publisher: New York (N.Y.): Springer,
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Mathematical analysis --- Calculus --- Problems, exercises, etc --- 517.1 --- -681.3*W1 --- 517 --- 517.2/.3 --- Analyse (wiskunde) --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions --- Geometry, Infinitesimal --- Introduction to analysis --- Computerwetenschap--?*W1 --- Problems, exercises, etc. --- 517.1 Introduction to analysis --- 681.3*W1 --- Calculus - Problems, exercises, etc
ISBN: 0387216499 0387986545 Year: 2002 Publisher: New York, United States : Springer,
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This book is a significant update of the first four chapters of Symmetries and Differential Equations (1989; reprinted with corrections, 1996), by George W. Bluman and Sukeyuki Kumei. Since 1989 there have been considerable developments in symmetry methods (group methods) for differential equations as evidenced by the number of research papers, books, and new symbolic manipulation software devoted to the subject. This is, no doubt, due to the inherent applicability of the methods to nonlinear differential equations. Symmetry methods for differential equations, originally developed by Sophus Lie in the latter half of the nineteenth century, are highly algorithmic and hence amenable to symbolic computation. These methods systematically unify and extend well-known ad hoc techniques to construct explicit solutions for differential equations, especially for nonlinear differential equations. Often ingenious tricks for solving particular differential equations arise transparently from the symmetry point of view, and thus it remains somewhat surprising that symmetry methods are not more widely known. Nowadays it is essential to learn the methods presented in this book to understand existing symbolic manipulation software for obtaining analytical results for differential equations. For ordinary differential equations (ODEs), these include reduction of order through group invariance or integrating factors. For partial differential equations (PDEs), these include the construction of special solutions such as similarity solutions or nonclassical solutions, finding conservation laws, equivalence mappings, and linearizations.
Differential equations --- Differential equations, Partial --- Lie groups. --- Numerical solutions. --- Mathematics. --- Global analysis (Mathematics). --- Applications of Mathematics. --- Theoretical, Mathematical and Computational Physics. --- Analysis. --- Applied mathematics. --- Engineering mathematics. --- Mathematical physics. --- Mathematical analysis. --- Analysis (Mathematics). --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- 517.91 Differential equations --- Numerical analysis
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ISBN: 0387969969 1475743092 1475743076 9780387969961 Year: 1989 Volume: 81 Publisher: New York: Springer,
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Ordinary differential equations --- Partial differential equations --- Differential equations --- Equations différentielles --- Differential equations, Partial --- Numerical solutions --- Lie groups. --- Numerical solutions. --- Equations différentielles --- Differential equations - Numerical solutions --- Differential equations, Partial - Numerical solutions
ISBN: 0387901078 3540901078 1461263948 9783540901075 9780387901077 Year: 1974 Volume: 13 Publisher: New York (N.Y.): Springer,
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Differential equations --- Differential equations, Partial --- Similarity transformations --- Series, Lie --- Numerical solutions --- -Differential equations, Partial --- -Series, Lie --- Similarity (Geometry) --- Transformations (Mathematics) --- Lie series --- Functions of complex variables --- Partial differential equations --- Equations, Differential --- Bessel functions --- Calculus --- Series, Lie. --- Similarity transformations. --- Numerical solutions. --- 517.91 Differential equations --- Numerical analysis --- 517.91 --- Resemblance (Philosophy) --- Similitude (physique) --- Lie, Séries de --- Numerical solutions&delete& --- Lie, Séries de --- Differential equations, Partial - Numerical solutions --- Differential equations - Numerical solutions --- Equations differentielles ordinaires --- Equations aux derivees partielles --- Methodes numeriques
Book
ISBN: 038798612X 1461424984 9786612834745 1282834746 0387680284 Year: 2010 Publisher: New York : Springer,
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This is an accessible book on advanced symmetry methods for partial differential equations. Topics include conservation laws, local symmetries, higher-order symmetries, contact transformations, delete "adjoint symmetries," Noether’s theorem, local mappings, nonlocally related PDE systems, potential symmetries, nonlocal symmetries, nonlocal conservation laws, nonlocal mappings, and the nonclassical method. Graduate students and researchers in mathematics, physics, and engineering will find this book useful. This book is a sequel to Symmetry and Integration Methods for Differential Equations (2002) by George W. Bluman and Stephen C. Anco. The emphasis in the present book is on how to find systematically symmetries (local and nonlocal) and conservation laws (local and nonlocal) of a given PDE system and how to use systematically symmetries and conservation laws for related applications.
Differential equations -- Numerical solutions. --- Differential equations, Partial -- Numerical solutions. --- Symmetry (Physics). --- Differential equations, Partial --- Differential equations --- Symmetry (Physics) --- Mathematics --- Algebra --- Calculus --- Mathematical Theory --- Physical Sciences & Mathematics --- Numerical solutions --- Numerical solutions. --- Invariance principles (Physics) --- Symmetry (Chemistry) --- 517.91 Differential equations --- Mathematics. --- Topological groups. --- Lie groups. --- Mathematical analysis. --- Analysis (Mathematics). --- Topological Groups, Lie Groups. --- Analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Math --- Science --- Conservation laws (Physics) --- Physics --- Numerical analysis --- Topological Groups. --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic
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ISBN: 9780387680286 9780387571935 9780387986128 9781461424987 Year: 2010 Publisher: New York, NY Springer
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This is an accessible book on advanced symmetry methods for partial differential equations. Topics include conservation laws, local symmetries, higher-order symmetries, contact transformations, delete "adjoint symmetries," Noether’s theorem, local mappings, nonlocally related PDE systems, potential symmetries, nonlocal symmetries, nonlocal conservation laws, nonlocal mappings, and the nonclassical method. Graduate students and researchers in mathematics, physics, and engineering will find this book useful. This book is a sequel to Symmetry and Integration Methods for Differential Equations (2002) by George W. Bluman and Stephen C. Anco. The emphasis in the present book is on how to find systematically symmetries (local and nonlocal) and conservation laws (local and nonlocal) of a given PDE system and how to use systematically symmetries and conservation laws for related applications.
Ordered algebraic structures --- Topological groups. Lie groups --- Mathematical analysis --- Mathematics --- analyse (wiskunde) --- topologie (wiskunde) --- wiskunde --- topologie
Book
ISBN: 9780387680286 9780387571935 9780387986128 9781461424987 Year: 2010 Publisher: New York NY Springer New York
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This is an accessible book on advanced symmetry methods for partial differential equations. Topics include conservation laws, local symmetries, higher-order symmetries, contact transformations, delete "adjoint symmetries," Noether's theorem, local mappings, nonlocally related PDE systems, potential symmetries, nonlocal symmetries, nonlocal conservation laws, nonlocal mappings, and the nonclassical method. Graduate students and researchers in mathematics, physics, and engineering will find this book useful. This book is a sequel to Symmetry and Integration Methods for Differential Equations (2002) by George W. Bluman and Stephen C. Anco. The emphasis in the present book is on how to find systematically symmetries (local and nonlocal) and conservation laws (local and nonlocal) of a given PDE system and how to use systematically symmetries and conservation laws for related applications.
Ordered algebraic structures --- Topological groups. Lie groups --- Mathematical analysis --- Mathematics --- analyse (wiskunde) --- topologie (wiskunde) --- wiskunde --- topologie
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