Involution : The Formal Theory of Differential Equations and its Applications in Computer Algebra

Werner M. Seiler

ISBN 10: 3642261353 / ISBN 13: 9783642261350

Published by Springer Berlin Heidelberg, 2012

About this Item

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.

Seller Inventory # 9783642261350

Bibliographic Details

• Title: Involution : The Formal Theory of Differential Equations and its Applications in Computer Algebra
• Publisher: Springer Berlin Heidelberg
• Publication Date: 2012
• Language: English
• ISBN 10: 3642261353
• ISBN 13: 9783642261350
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 36D millimeters 235 millimeters width by 155 millimeters height by 36 millimeters depth
• Weight: 1001 grams

About this title

Synopsis

The book provides a self-contained account of the formal theory of general, i.e. also under- and overdetermined, systems of differential equations which in its central notion of involution combines geometric, algebraic, homological and combinatorial ideas.

About the Author

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.