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024 7 $a10.1007/978-3-642-34035-2
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035   $a(DE-He213)978-3-642-34035-2
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100   $a20121215d2013      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aComposite Asymptotic Expansions$b[electronic resource] /$fby Augustin Fruchard, Reinhard Schafke
205   $a1st ed. 2013.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2013.
215   $a1 online resource (X, 161 p. 21 illus.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2066
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-642-34034-2 
320   $aIncludes bibliographical references and index.
327   $aFour Introductory Examples -- Composite Asymptotic Expansions: General Study -- Composite Asymptotic Expansions: Gevrey Theory -- A Theorem of Ramis-Sibuya Type -- Composite Expansions and Singularly Perturbed Differential Equations -- Applications -- Historical Remarks -- References -- Index.
330   $aThe purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansions near turning points. Thus our approach is closely related to the method of matched asymptotic expansions. CAsEs offer two unique advantages, however. First, they provide uniform expansions near a turning point and away from it. Second, a Gevrey version of CAsEs is available and detailed in the lecture notes. Three problems are presented in which CAsEs are useful. The first application concerns canard solutions near a multiple turning point. The second application concerns so-called non-smooth or angular canard solutions. Finally an Ackerberg-O?Malley resonance problem is solved.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v2066
606   $aApproximation theory
606   $aDifferential equations
606   $aSequences (Mathematics)
606   $aApproximations and Expansions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12023
606   $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147
606   $aSequences, Series, Summability$3https://scigraph.springernature.com/ontologies/product-market-codes/M1218X
615  0$aApproximation theory.
615  0$aDifferential equations.
615  0$aSequences (Mathematics).
615 14$aApproximations and Expansions.
615 24$aOrdinary Differential Equations.
615 24$aSequences, Series, Summability.
676   $a511.4
686   $a41A60$a34E$a34M30$a34M60$2msc
700   $aFruchard$b Augustin$4aut$4http://id.loc.gov/vocabulary/relators/aut$0479689
702   $aSchafke$b Reinhard$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a996466770503316
996   $aComposite Asymptotic Expansions$92510957
997   $aUNISA