000			03018nam a22004935i 4500
001			978-3-642-34035-2
003			DE-He213
005			20140220082856.0
007			cr nn 008mamaa
008			121215s2013 gw | s |||| 0|eng d
020			_a9783642340352 _9978-3-642-34035-2
024	7		_a10.1007/978-3-642-34035-2 _2doi
050		4	_aQA401-425
072		7	_aPBKJ _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a511.4 _223
100	1		_aFruchard, Augustin. _eauthor.
245	1	0	_aComposite Asymptotic Expansions _h[electronic resource] / _cby Augustin Fruchard, Reinhard Schäfke.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2013.
300			_aX, 161 p. 21 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aLecture Notes in Mathematics, _x0075-8434 ; _v2066
505	0		_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.
520			_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.
650		0	_aMathematics.
650		0	_aDifferential Equations.
650		0	_aSequences (Mathematics).
650	1	4	_aMathematics.
650	2	4	_aApproximations and Expansions.
650	2	4	_aOrdinary Differential Equations.
650	2	4	_aSequences, Series, Summability.
700	1		_aSchäfke, Reinhard. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642340345
830		0	_aLecture Notes in Mathematics, _x0075-8434 ; _v2066
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-642-34035-2
912			_aZDB-2-SMA
912			_aZDB-2-LNM
999			_c97462 _d97462