04261nam 22007455 450 991029997720332120200701205324.01-4471-6398-210.1007/978-1-4471-6398-5(CKB)3710000000094949(Springer)9781447163985(MH)013990575-8(SSID)ssj0001187405(PQKBManifestationID)11697461(PQKBTitleCode)TC0001187405(PQKBWorkID)11244038(PQKB)11173999(DE-He213)978-1-4471-6398-5(MiAaPQ)EBC3101247(PPN)177825138(EXLCZ)99371000000009494920140306d2014 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierOrdinary Differential Equations[electronic resource] Analysis, Qualitative Theory and Control /by Hartmut Logemann, Eugene P. Ryan1st ed. 2014.London :Springer London :Imprint: Springer,2014.1 online resource (XIII, 333 p. 40 illus.)online resourceSpringer Undergraduate Mathematics Series,1615-2085Bibliographic Level Mode of Issuance: Monograph1-4471-6397-4 Includes bibliographical references (pages 327-328) and index.Introduction -- Linear differential equations -- Introduction to linear control theory -- Nonlinear differential equations -- Stability and asymptotic behaviour -- Stability of feedback systems and stabilization.The book comprises a rigorous and self-contained treatment of initial-value problems for ordinary differential equations. It additionally develops the basics of control theory, which is a unique feature in the current textbook literature. The following topics are particularly emphasised: • existence, uniqueness and continuation of solutions, • continuous dependence on initial data, • flows, • qualitative behaviour of solutions, • limit sets, • stability theory, • invariance principles, • introductory control theory, • feedback and stabilization. The last two items cover classical control theoretic material such as linear control theory and absolute stability of nonlinear feedback systems. It also includes an introduction to the more recent concept of input-to-state stability. Only a basic grounding in linear algebra and analysis is assumed. Ordinary Differential Equations will be suitable for final year undergraduate students of mathematics and appropriate for beginning postgraduates in mathematics and in mathematically oriented engineering and science.Springer Undergraduate Mathematics Series,1615-2085Differential equationsSystem theoryVibrationDynamical systemsDynamicsOrdinary Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12147Systems Theory, Controlhttps://scigraph.springernature.com/ontologies/product-market-codes/M13070Vibration, Dynamical Systems, Controlhttps://scigraph.springernature.com/ontologies/product-market-codes/T15036Differential equations.System theory.Vibration.Dynamical systems.Dynamics.Ordinary Differential Equations.Systems Theory, Control.Vibration, Dynamical Systems, Control.515/.35Logemann Hartmutauthttp://id.loc.gov/vocabulary/relators/aut721761Ryan Eugene Pauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910299977203321Ordinary Differential Equations2512151UNINAThis Record contains information from the Harvard Library Bibliographic Dataset, which is provided by the Harvard Library under its Bibliographic Dataset Use Terms and includes data made available by, among others the Library of Congress