LEADER 04171nam 22006495 450 001 9910254091003321 005 20200701020936.0 010 $a1-4939-6389-9 024 7 $a10.1007/978-1-4939-6389-8 035 $a(CKB)3710000001006469 035 $a(DE-He213)978-1-4939-6389-8 035 $a(MiAaPQ)EBC6312200 035 $a(MiAaPQ)EBC5576262 035 $a(Au-PeEL)EBL5576262 035 $a(OCoLC)1066195228 035 $a(PPN)197134319 035 $a(EXLCZ)993710000001006469 100 $a20161111d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aOrdinary Differential Equations: Basics and Beyond /$fby David G. Schaeffer, John W. Cain 205 $a1st ed. 2016. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2016. 215 $a1 online resource (XXX, 542 p. 139 illus., 61 illus. in color.) 225 1 $aTexts in Applied Mathematics,$x0939-2475 ;$v65 311 $a1-4939-6387-2 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- Linear Systems with Constant Coefficients -- Nonlinear Systems: Local Theory -- Nonlinear Systems: Global Theory -- Nondimensionalization and Scaling -- Trajectories Near Equilibria -- Oscillations in ODEs -- Bifurcation from Equilibria -- Examples of Global Bifurcation -- Epilogue -- Appendices. 330 $aThis book develops the theory of ordinary differential equations (ODEs), starting from an introductory level (with no prior experience in ODEs assumed) through to a graduate-level treatment of the qualitative theory, including bifurcation theory (but not chaos). While proofs are rigorous, the exposition is reader-friendly, aiming for the informality of face-to-face interactions. A unique feature of this book is the integration of rigorous theory with numerous applications of scientific interest. Besides providing motivation, this synthesis clarifies the theory and enhances scientific literacy. Other features include: (i) a wealth of exercises at various levels, along with commentary that explains why they matter; (ii) figures with consistent color conventions to identify nullclines, periodic orbits, stable and unstable manifolds; and (iii) a dedicated website with software templates, problem solutions, and other resources supporting the text. Given its many applications, the book may be used comfortably in science and engineering courses as well as in mathematics courses. Its level is accessible to upper-level undergraduates but still appropriate for graduate students. The thoughtful presentation, which anticipates many confusions of beginning students, makes the book suitable for a teaching environment that emphasizes self-directed, active learning (including the so-called inverted classroom). 410 0$aTexts in Applied Mathematics,$x0939-2475 ;$v65 606 $aDifferential equations 606 $aMathematical physics 606 $aDynamics 606 $aErgodic theory 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aTheoretical, Mathematical and Computational Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19005 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 615 0$aDifferential equations. 615 0$aMathematical physics. 615 0$aDynamics. 615 0$aErgodic theory. 615 14$aOrdinary Differential Equations. 615 24$aTheoretical, Mathematical and Computational Physics. 615 24$aDynamical Systems and Ergodic Theory. 676 $a515.352 700 $aSchaeffer$b David G$4aut$4http://id.loc.gov/vocabulary/relators/aut$021355 702 $aCain$b John W$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254091003321 996 $aOrdinary Differential Equations: Basics and Beyond$92162705 997 $aUNINA