000 03549nam a22004935i 4500
001 978-1-4614-5477-9
003 DE-He213
005 20140220082820.0
007 cr nn 008mamaa
008 121205s2013 xxu| s |||| 0|eng d
020 _a9781461454779
_9978-1-4614-5477-9
024 7 _a10.1007/978-1-4614-5477-9
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.353
_223
100 1 _aHolmes, Mark H.
_eauthor.
245 1 0 _aIntroduction to Perturbation Methods
_h[electronic resource] /
_cby Mark H. Holmes.
250 _a2nd ed. 2013.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aXVII, 436 p. 117 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aTexts in Applied Mathematics,
_x0939-2475 ;
_v20
505 0 _aPreface -- Preface to Second Edition -- Introduction to Asymptotic Approximations -- Matched Asymptotic Expansions -- Multiple Scales -- The WKB and Related Methods -- The Method of Homogenization- Introduction to Bifurcation and Stability -- References -- Index.
520 _aThis introductory graduate text is based on a graduate course the author has taught repeatedly over the last twenty or so years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover more advanced topics such as systems and partial differential equations. Moreover, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations.  Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.  For this new edition every section has been updated throughout, many only in minor ways, while others have been completely rewritten. New material has also been added. This includes approximations for weakly coupled oscillators, analysis of problems that involve transcendentally small terms, an expanded discussion of Kummer functions, and metastability. Two appendices have been added, one on solving difference equations and another on delay equations. Additional exercises have been included throughout.  Review of first edition: "Those familiar with earlier expositions of singular perturbations for ordinary and partial differential equations will find many traditional gems freshly presented, as well as many new topics. Much of the excitement lies in the examples and the more than 250 exercises, which are guaranteed to provoke and challenge readers and learners with various backgrounds and levels of expertise." (SIAM Review, 1996 )  
650 0 _aMathematics.
650 0 _aGlobal analysis (Mathematics).
650 0 _aDifferential Equations.
650 0 _aDifferential equations, partial.
650 1 4 _aMathematics.
650 2 4 _aPartial Differential Equations.
650 2 4 _aOrdinary Differential Equations.
650 2 4 _aAnalysis.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461454762
830 0 _aTexts in Applied Mathematics,
_x0939-2475 ;
_v20
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-5477-9
912 _aZDB-2-SMA
999 _c95420
_d95420