LEADER 04261nam 22007455 450 001 9910299977203321 005 20200701205324.0 010 $a1-4471-6398-2 024 7 $a10.1007/978-1-4471-6398-5 035 $a(CKB)3710000000094949 035 $a(Springer)9781447163985 035 $a(MH)013990575-8 035 $a(SSID)ssj0001187405 035 $a(PQKBManifestationID)11697461 035 $a(PQKBTitleCode)TC0001187405 035 $a(PQKBWorkID)11244038 035 $a(PQKB)11173999 035 $a(DE-He213)978-1-4471-6398-5 035 $a(MiAaPQ)EBC3101247 035 $a(PPN)177825138 035 $a(EXLCZ)993710000000094949 100 $a20140306d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aOrdinary Differential Equations$b[electronic resource] $eAnalysis, Qualitative Theory and Control /$fby Hartmut Logemann, Eugene P. Ryan 205 $a1st ed. 2014. 210 1$aLondon :$cSpringer London :$cImprint: Springer,$d2014. 215 $a1 online resource (XIII, 333 p. 40 illus.)$conline resource 225 1 $aSpringer Undergraduate Mathematics Series,$x1615-2085 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a1-4471-6397-4 320 $aIncludes bibliographical references (pages 327-328) and index. 327 $aIntroduction -- Linear differential equations -- Introduction to linear control theory -- Nonlinear differential equations -- Stability and asymptotic behaviour -- Stability of feedback systems and stabilization. 330 $aThe book comprises a rigorous and self-contained treatment of initial-value problems for ordinary differential equations. It additionally develops the basics of control theory, which is a unique feature in the current textbook literature. The following topics are particularly emphasised: ? existence, uniqueness and continuation of solutions, ? continuous dependence on initial data, ? flows, ? qualitative behaviour of solutions, ? limit sets, ? stability theory, ? invariance principles, ? introductory control theory, ? feedback and stabilization. The last two items cover classical control theoretic material such as linear control theory and absolute stability of nonlinear feedback systems. It also includes an introduction to the more recent concept of input-to-state stability. Only a basic grounding in linear algebra and analysis is assumed. Ordinary Differential Equations will be suitable for final year undergraduate students of mathematics and appropriate for beginning postgraduates in mathematics and in mathematically oriented engineering and science. 410 0$aSpringer Undergraduate Mathematics Series,$x1615-2085 606 $aDifferential equations 606 $aSystem theory 606 $aVibration 606 $aDynamical systems 606 $aDynamics 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070 606 $aVibration, Dynamical Systems, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/T15036 615 0$aDifferential equations. 615 0$aSystem theory. 615 0$aVibration. 615 0$aDynamical systems. 615 0$aDynamics. 615 14$aOrdinary Differential Equations. 615 24$aSystems Theory, Control. 615 24$aVibration, Dynamical Systems, Control. 676 $a515/.35 700 $aLogemann$b Hartmut$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721761 702 $aRyan$b Eugene P$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299977203321 996 $aOrdinary Differential Equations$92512151 997 $aUNINA 999 $aThis 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