03173nam a22005055i 4500001001800000003000900018005001700027007001500044008004100059020001800100024002500118041000800143050001400151050001400165072001600179072002300195082001200218100002800230245015200258260003800410264003800448300003400486336002600520337002600546338003600572347002400608505017300632520136800805650001702173650002802190650001702218650002602235650002902261650002702290650001702317650005902334650003302393650004402426650003202470650003702502710003402539773002002573776003602593856003802629978-0-387-23217-1DE-He21320141014113427.0cr nn 008mamaa100301s2005 xxu| s |||| 0|eng d a97803872321717 a10.1007/b1009572doi aeng 4aTA329-348 4aTA640-643 7aTBJ2bicssc 7aMAT0030002bisacsh04a5192231 aJohnson, R. S.eauthor.10aSingular Perturbation Theoryh[electronic resource] :bMathematical and Analytical Techniques with Applications to Engineering /cby R. S. Johnson. 1aBoston, MA :bSpringer US,c2005. 1aBoston, MA :bSpringer US,c2005. aXVI, 292 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aMathematical Preliminaries -- Introductory Applications -- Further Applications -- The Method of Multiple Scales -- Some Worked Examples Arising from Physical Problems. aMany areas of science and engineering produce difficult mathematical problems , i.e., problems that cannot be solved in any conventional sense. In many cases, against all the apparent odds, it is possible to construct systematic approximations that lead to useful solutions. The most powerful of these approximation techniques is singular perturbation theory. Singular Perturbation Theory introduces all the background ideas to this subject, designed for those with only the most superficial familiarity with university-level mathematics. The methods are developed through worked examples and set exercises (with answers); the latter part of the book is devoted to applications drawn from: mechanics, physics, semi- and superconductor theory, fluid mechanics, thermal processes, chemical and biochemical reactions. In a novel approach, these are grouped together so that the reader with particular interests can readily access them. This book is based on material that has been taught, mainly by the author, to MSc and research students in applied mathematics and engineering mathematics at the University of Newcastle upon Tyne over the last thirty years. The aim of this text is to make all the material readily accessible to the reader who wishes to learn and use the ideas to help with research problems and who does not have a strong mathematical background. 0aEngineering. 0aDifferential Equations. 0aMathematics. 0aMathematical physics. 0aEngineering mathematics. 0aHydraulic engineering.14aEngineering.24aAppl.Mathematics/Computational Methods of Engineering.24aApplications of Mathematics.24aMathematical and Computational Physics.24aEngineering Fluid Dynamics.24aOrdinary Differential Equations.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z978038723200340uhttp://dx.doi.org/10.1007/b100957