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020 _a9783319095707
_9978-3-319-09570-7
024 7 _a10.1007/978-3-319-09570-7
_2doi
050 4 _aQA372
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
072 7 _aPBKJ
_2thema
082 0 4 _a515.352
_223
100 1 _aShchepakina, Elena.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aSingular Perturbations
_h[electronic resource] :
_bIntroduction to System Order Reduction Methods with Applications /
_cby Elena Shchepakina, Vladimir Sobolev, Michael P. Mortell.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2014.
300 _aXIII, 212 p. 50 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 ;
_v2114
505 0 _aIntroduction -- Slow Integral Manifolds -- The Book of Numbers -- Representations of Slow Integral Manifolds -- Singular Singularly Perturbed Systems -- Reduction Methods for Chemical Systems -- Specific Cases -- Canards and Black Swans -- Appendix: Proofs.
520 _aThese lecture notes provide a fresh approach to investigating singularly perturbed systems using asymptotic and geometrical techniques. It gives many examples and step-by-step techniques, which will help beginners move to a more advanced level. Singularly perturbed systems appear naturally in the modelling of many processes that are characterized by slow and fast motions simultaneously, for example, in fluid dynamics and nonlinear mechanics. This book’s approach consists in separating out the slow motions of the system under investigation. The result is a reduced differential system of lesser order. However, it inherits the essential elements of the qualitative behaviour of the original system. Singular Perturbations differs from other literature on the subject due to its methods and wide range of applications. It is a valuable reference for specialists in the areas of applied mathematics, engineering, physics, biology, as well as advanced undergraduates for the earlier parts of the book, and graduate students for the later chapters.
650 0 _aDifferential Equations.
650 0 _aDifferentiable dynamical systems.
650 0 _aEngineering mathematics.
650 0 _aEngineering.
650 1 4 _aOrdinary Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12147
650 2 4 _aDynamical Systems and Ergodic Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M1204X
650 2 4 _aMathematical Applications in the Physical Sciences.
_0http://scigraph.springernature.com/things/product-market-codes/M13120
650 2 4 _aMathematical and Computational Biology.
_0http://scigraph.springernature.com/things/product-market-codes/M31000
650 2 4 _aMathematical and Computational Engineering.
_0http://scigraph.springernature.com/things/product-market-codes/T11006
650 2 4 _aEngineering Thermodynamics, Heat and Mass Transfer.
_0http://scigraph.springernature.com/things/product-market-codes/T14000
700 1 _aSobolev, Vladimir.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aMortell, Michael P.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319095714
776 0 8 _iPrinted edition:
_z9783319095691
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2114
856 4 0 _uhttps://doi.org/10.1007/978-3-319-09570-7
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c12263
_d12263