03395nam 22006375 450 991029999460332120250609111204.03-319-11924-910.1007/978-3-319-11924-3(CKB)3710000000306144(SSID)ssj0001386537(PQKBManifestationID)11883500(PQKBTitleCode)TC0001386537(PQKBWorkID)11374014(PQKB)11510349(DE-He213)978-3-319-11924-3(MiAaPQ)EBC6312608(MiAaPQ)EBC5595322(Au-PeEL)EBL5595322(OCoLC)899249029(PPN)183089626(MiAaPQ)EBC2001802(EXLCZ)99371000000030614420141119d2014 u| 0engurnn|008mamaatxtccrHistorical Developments in Singular Perturbations /by Robert E. O'Malley1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (X, 256 p. 17 illus.) Bibliographic Level Mode of Issuance: Monograph3-319-11923-0 Preface -- Ludwig Prandtl's Boundary Layer Theory -- Asymptotic Approximations -- The Method of Matches Asymptotic Expansions and Its Generalizations -- Wendepunkts and Canards (Turning Points and Delayed Bifurcations) -- Two-timing, Geometric, and Multi-scale Methods -- A Simple Multi-scale Procedure for Both Oscillatory and Boundary Layer Problems -- References -- Index.This engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status. While the approach of the text is sophisticated, the literature is accessible to a broad audience. A particularly valuable bonus are the historical remarks. These remarks are found throughout the manuscript. They demonstrate the growth of mathematical thinking on this topic by engineers and mathematicians. The book focuses on detailing how the various methods are to be applied. These are illustrated by a  number and variety of examples. Readers are expected to have a working knowledge of elementary ordinary differential equations, including some familiarity with power series techniques, and of some advanced calculus. Dr. O'Malley  has written a number of books on singular perturbations.  This book has developed from many of his works in the field of perturbation theory.Differential equationsMathematicsHistoryOrdinary Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12147History of Mathematical Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/M23009Differential equations.Mathematics.History.Ordinary Differential Equations.History of Mathematical Sciences.510O'Malley Robert Eauthttp://id.loc.gov/vocabulary/relators/aut40554MiAaPQMiAaPQMiAaPQBOOK9910299994603321Historical developments in singular perturbations1409939UNINA