03751nam 2200541 i 45000010014000000030005000140050017000190060019000360070015000550080041000700100031001110200030001420200025001720280015001970350025002120350021002370400040002580500025002980820016003231000027003392450054003662500021004202640150004413000059005913360021006503370026006713380032006974900042007295040051007715050293008225060072011155201447011875300037026345380036026715380047027075880054027546500059028086530036028676530022029036530010029256530017029356530016029526530016029687100064029847760053030488300043031018560065031449781611974645SIAM20170228190106.0m eo d cr bn |||m|||a170224s2017 paua ob 001 0 eng d a 2016053307z 2016052904 a9781611974645qelectronic z9781611974638qprint50aMM22bSIAM a(CaBNVSL)thg00972503 a(OCoLC)973929628 aCaBNVSLbengerdacCaBNVSLdCaBNVSL 4aQA614.8b.M45 2017eb04a515/.392231 aMeiss, J. D.,eauthor.10aDifferential dynamical systems /cJames D. Meiss. aRevised edition. 1aPhiladelphia, Pennsylvania :bSociety for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104),c[2017] a1 PDF (xvii, 392 pages) :billustrations (some color). atext2rdacontent aelectronic2isbdmedia aonline resource2rdacarrier1 aMathematical modeling and computation aIncludes bibliographical references and index.0 aPreface to the revised edition -- Preface -- 1. Introduction -- 2. Linear systems -- 3. Existence and uniqueness -- 4. Dynamical systems -- 5. Invariant manifolds -- 6. The phase plane -- 7. Chaotic dynamics -- 8. Bifurcation theory -- 9. Hamiltonian dynamics -- A. Mathematical software. aRestricted to subscribers or individual electronic text purchasers.3 aDifferential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics. Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts--flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. Revisions include simplified and clarified proofs of a number of theorems, an expanded introduction to function spaces, additional exercises, and the correction of typographical errors. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Mapleª, Mathematicaª, and MATLABª software to give students practice with computation applied to dynamical systems problems. aAlso available in print version. aMode of access: World Wide Web. aSystem requirements: Adobe Acrobat Reader. aDescription based on title page of print version. 0aDifferentiable dynamical systemsxMathematical models. aOrdinary differential equations aDynamical systems aChaos aNonlinearity aBifurcation aPhase space2 aSociety for Industrial and Applied Mathematics,epublisher.08iPrint version:w(DLC) 2016052904z9781611974638 0aMathematical modeling and computation.403SIAMuhttp://epubs.siam.org/doi/book/10.1137/1.9781611974645