03713nam 2200601 450 991013096510332120170816115255.01-283-30628-X97866133062891-118-03153-91-118-03328-0(CKB)3460000000080822(EBL)699924(OCoLC)778616746(SSID)ssj0000613383(PQKBManifestationID)11386649(PQKBTitleCode)TC0000613383(PQKBWorkID)10586919(PQKB)10017406(MiAaPQ)EBC699924(PPN)170219364(EXLCZ)99346000000008082220160816h20042004 uy 0engur|n|---|||||txtccrPrinciples of differential equations /Nelson G. MarkleyHoboken, New Jersey :John Wiley & Sons, Inc.,2004.©20041 online resource (354 p.)Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and TractsDescription based upon print version of record.0-471-64956-2 Includes bibliographical references and index.Principles of Differential Equations; Contents; Preface; 1 Fundamental Theorems; 1.1 Preliminaries; 1.2 Existence; 1.3 Uniqueness; 1.4 Numerical Approximation; 1.5 Continuation; 1.6 Continuity in Initial Conditions; 2 Classical Themes; 2.1 Integrals; 2.2 The Qualitative Point of View; 2.3 Differential Inequalities; 3 Linear Differential Equations; 3.1 Elementary Properties; 3.2 Fundamental Matrix Solutions; 3.3 Higher Order Linear Differential Equations; 3.4 Complex Linear Differential Equations; 4 Constant Coefficients; 4.1 The Exponential of a Matrix; 4.2 Generalized Eigenspaces4.3 Canonical Forms4.4 Higher Order Equations; 4.5 The Range of the Exponential Map; 5 Stability; 5.1 Stability at Fixed Points; 5.2 Stability and Constant Coefficients; 5.3 Stability and General Linear Systems; 5.4 Linear Systems with Periodic Coefficients; 6 The Poincaré Return Map; 6.1 Local Sections; 6.2 Planar Dynamics; 6.3 Recurrence; 7 Smooth Vector Fields; 7.1 Differentiate Functions; 7.2 Differentiation in Initial Conditions; 7.3 Linearization; 7.4 Hamiltonian Systems; 8 Hyperbolic Phenomenon; 8.1 Hyperbolic Linear Vector Fields; 8.2 Perturbed Hyperbolic Systems8.3 The Contraction Mapping Principle8.4 Local Stable Manifolds; 9 Bifurcations; 9.1 The Implicit Function Theorem; 9.2 Persistence of Periodic Points; 9.3 Hopf Bifurcations; Bibliography; IndexAn accessible, practical introduction to the principles of differential equations The field of differential equations is a keystone of scientific knowledge today, with broad applications in mathematics, engineering, physics, and other scientific fields. Encompassing both basic concepts and advanced results, Principles of Differential Equations is the definitive, hands-on introduction professionals and students need in order to gain a strong knowledge base applicable to the many different subfields of differential equations and dynamical systems. Nelson Markley includes essential backgroundPure and applied mathematics (John Wiley & Sons : Unnumbered)Differential equationsDifferential equations.515.35515/.35Markley Nelson Groh1940-860608MiAaPQMiAaPQMiAaPQBOOK9910130965103321Principles of differential equations1920468UNINA