02783nam a2200397 i 4500991002949479707536160721s2014 sz a b 001 0 eng d9783319095691b14258869-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng515.35223AMS 34-02AMS 34C45AMS 34E15AMS 34E17LC QA372Shchepakina, Elena716378Singular perturbations :introduction to system order reduction methods with applications /by Elena Shchepakina, Vladimir Sobolev, Michael P. MortellCham [Switzerland] :Springer,c2014XIII, 212 p. :50 ill. ;24 cmLecture notes in mathematics,0075-8434 ;2114Introduction ; 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: ProofsThese 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 chaptersDifferentiable dynamical systemsDifferential equationsEngineering mathematicsEngineeringSobolev, Vladimirauthorhttp://id.loc.gov/vocabulary/relators/aut721500Mortell, Michael P.Springer eBooks.b1425886917-11-1621-07-16991002949479707536LE013 34-XX SHC11 (2014)12013000293561le013pE46.79-l- 00000.i1578747317-11-16Singular perturbations1465277UNISALENTOle01321-07-16ma -engsz 00