Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra (Algorithms and Computation in Mathematics, 24, Band 24) - Softcover
Buch 18 von 24: Algorithms and Computation in Mathematics
Inhaltsangabe
Formal Geometry of Differential Equations.- Involution I: Algebraic Theory.- Completion to Involution.- Structure Analysis of Polynomial Modules.- Involution II: Homological Theory.- Involution III: Differential Theory.- The Size of the Formal Solution Space.- Existence and Uniqueness of Solutions.- Linear Differential Equations.- Miscellaneous.- Algebra.- Differential Geometry.
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Über die Autorin bzw. den Autor
W.M. Seiler is professor for computational mathematics (algorithmic algebra) at Kassel University. His research fields include differential equations, commutative algebra and mechanics. He is particularly interested in combining geometric and algebraic approaches. For many years, he has been an external developer for the computer algebra system MuPAD.
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Involution
ISBN 10: 3642261353
ISBN 13: 9783642261350
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Taschenbuch. Zustand: Neu. Neuware -As long as algebra and geometry proceeded along separate paths, their advance was slow and their applications limited. But when these sciences joined company they drew from each other fresh vitality and thenceforward marched on at rapid pace towards perfection Joseph L. Lagrange The theory of differential equations is one of the largest elds within mathematics and probably most graduates in mathematics have attended at least one course on differentialequations. But differentialequationsare also offundamentalimportance in most applied sciences; whenever a continuous process is modelled mathem- ically, chances are high that differential equations appear. So it does not surprise that many textbooks exist on both ordinary and partial differential equations. But the huge majority of these books makes an implicit assumption on the structure of the equations: either one deals with scalar equations or with normal systems, i. e. with systems in Cauchy¿Kovalevskaya form. The main topic of this book is what happens, if this popular assumption is dropped. This is not just an academic exercise; non-normal systems are ubiquitous in - plications. Classical examples include the incompressible Navier¿Stokes equations of uid dynamics, Maxwell¿s equations of electrodynamics, the Yang¿Mills eq- tions of the fundamental gauge theories in modern particle physics or Einstein¿s equations of general relativity. But also the simulation and control of multibody systems, electrical circuits or chemical reactions lead to non-normal systems of - dinary differential equations, often called differential algebraic equations. In fact, most of the differentialequationsnowadaysencounteredby engineersand scientists are probably not normal.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 672 pp. Englisch. Artikel-Nr. 9783642261350
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Involution : The Formal Theory of Differential Equations and its Applications in Computer Algebra
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - As long as algebra and geometry proceeded along separate paths, their advance was slow and their applications limited. But when these sciences joined company they drew from each other fresh vitality and thenceforward marched on at rapid pace towards perfection Joseph L. Lagrange The theory of differential equations is one of the largest elds within mathematics and probably most graduates in mathematics have attended at least one course on differentialequations. But differentialequationsare also offundamentalimportance in most applied sciences; whenever a continuous process is modelled mathem- ically, chances are high that differential equations appear. So it does not surprise that many textbooks exist on both ordinary and partial differential equations. But the huge majority of these books makes an implicit assumption on the structure of the equations: either one deals with scalar equations or with normal systems, i. e. with systems in Cauchy Kovalevskaya form. The main topic of this book is what happens, if this popular assumption is dropped. This is not just an academic exercise; non-normal systems are ubiquitous in - plications. Classical examples include the incompressible Navier Stokes equations of uid dynamics, Maxwell s equations of electrodynamics, the Yang Mills eq- tions of the fundamental gauge theories in modern particle physics or Einstein s equations of general relativity. But also the simulation and control of multibody systems, electrical circuits or chemical reactions lead to non-normal systems of - dinary differential equations, often called differential algebraic equations. In fact, most of the differentialequationsnowadaysencounteredby engineersand scientists are probably not normal. Artikel-Nr. 9783642261350
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Involution: The Formal Theory of Differential Equations and Its Applications in Computer Algebra
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Paperback. Zustand: Brand New. reprint edition. 650 pages. 8.75x6.00x1.75 inches. In Stock. Artikel-Nr. x-3642261353
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