03518nam 22005775i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003100137050001000168072001700178072002300195082001600218100003400234245015500268264004600423300003400469336002600503337002600529338003600555347002400591490005100615505041200666520113501078650001702213650001402230650002002244650002802264650003602292650002502328650002902353650002402382650001302406650001702419650003702436650003602473650003702509650004202546650002402588650003302612710003402645773002002679776003602699830005102735856004402786912001402830999001902844952007702863978-0-387-28313-5DE-He21320180115171355.0cr nn 008mamaa100301s2005 xxu| s |||| 0|eng d a97803872831359978-0-387-28313-57 a10.1007/0-387-28313-72doi 4aQA372 7aPBKJ2bicssc 7aMAT0070002bisacsh04a515.3522231 aVerhulst, Ferdinand.eauthor.10aMethods and Applications of Singular Perturbationsh[electronic resource] :bBoundary Layers and Multiple Timescale Dynamics /cby Ferdinand Verhulst. 1aNew York, NY :bSpringer New York,c2005. aXVI, 328 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aTexts in Applied Mathematics,x0939-2475 ;v500 aBasic Material -- Approximation of Integrals -- Boundary Layer Behaviour -- Two-Point Boundary Value Problems -- Nonlinear Boundary Value Problems -- Elliptic Boundary Value Problems -- Boundary Layers in Time -- Evolution Equations with Boundary Layers -- The Continuation Method -- Averaging and Timescales -- Advanced Averaging -- Averaging for Evolution Equations -- Wave Equations on Unbounded Domains. aPerturbation theory, one of the most intriguing and essential topics in mathematics, and its applications to the natural and engineering sciences is the main focus of this workbook. In a systematic introductory manner, this unique book deliniates boundary layer theory for ordinary and partial differential equations, multi-timescale phenomena for nonlinear oscillations, diffusion and nonlinear wave equations. The book provides analysis of simple examples in the context of the general theory, as well as a final discussion of the more advanced problems. Precise estimates and excursions into the theoretical background makes this workbook valuable to both the applied sciences and mathematics fields. As a bonus in its last chapter the book includes a collection of rare and useful pieces of literature, such as the summary of the Perturbation theory of Matrices. Detailed illustrations, stimulating examples and exercises as well as a clear explanation of the underlying theory makes this workbook ideal for senior undergraduate and beginning graduate students in applied mathematics as well as science and engineering fields. 0aMathematics. 0aDynamics. 0aErgodic theory. 0aDifferential equations. 0aPartial differential equations. 0aApplied mathematics. 0aEngineering mathematics. 0aNumerical analysis. 0aPhysics.14aMathematics.24aOrdinary Differential Equations.24aPartial Differential Equations.24aMathematical Methods in Physics.24aDynamical Systems and Ergodic Theory.24aNumerical Analysis.24aApplications of Mathematics.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780387229669 0aTexts in Applied Mathematics,x0939-2475 ;v5040uhttp://dx.doi.org/10.1007/0-387-28313-7 aZDB-2-SMA c369352d369352 001040708EBookaelibbelibd2018-01-15r2018-01-15w2018-01-15yEBOOK