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Author Shchepakina, Elena, author

Title Singular perturbations : introduction to system order reduction methods with applications / Elena Shchepakina, Vladimir Sobolev, Michael P. Mortell
Published Cham [Switzerland] : Springer, [2014]
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Description 1 online resource (xiii, 212 pages) : illustrations
Series Lecture notes in mathematics, 1617-9692 ; 2114
Lecture notes in mathematics (Springer-Verlag) ; 2114
Contents Introduction -- Slow Integral Manifolds -- The Book of Numbers -- Representations of Slow Integral Manifolds -- Singular Singularly Perturbed Systems -- Reduction Methods for Chemical Systems -- Specific Cases -- Canards and Black Swans -- Appendix: Proofs
Summary These lecture notes provide a fresh approach to investigating singularly perturbed systems using asymptotic and geometrical techniques. It gives many examples and step-by-step techniques, which will help beginners move to a more advanced level. Singularly perturbed systems appear naturally in the modelling of many processes that are characterized by slow and fast motions simultaneously, for example, in fluid dynamics and nonlinear mechanics. This book?s approach consists in separating out the slow motions of the system under investigation. The result is a reduced differential system of lesser order. However, it inherits the essential elements of the qualitative behaviour of the original system. Singular Perturbations differs from other literature on the subject due to its methods and wide range of applications. It is a valuable reference for specialists in the areas of applied mathematics, engineering, physics, biology, as well as advanced undergraduates for the earlier parts of the book, and graduate students for the later chapters
Bibliography Includes bibliographical references and index
Notes Online resource; title from PDF title page (SpringerLink, viewed October 13, 2014)
Subject Singular perturbations (Mathematics)
Form Electronic book
Author Sobolev, Vladimir, author
Mortell, Michael P., author
ISBN 3319095706 (electronic bk.)
9783319095707 (electronic bk.)