03070nam a22003497i 4500003000400000005001700004008004100021020003100062040001800093050002400111100003400135245009400169264003400263264001100297300004600308336002600354337002800380338002700408490005400435500003500489504005100524505031800575520146400893650002802357650005402385700004502439830004302484856004102527942001202568999001702580952012302597URS20220117094655.0181206b ||||| |||| 00| 0 eng d a9781493963874 (alk. paper) bengerdacURS00aQA 371bSch136 20161 aSchaeffer, David G.,eauthor.10aOrdinary differential equations :bbasics and beyond /cDavid G. Schaeffer, John W. Cain. 1aNew York :bSpringer,c[2016] 4c©2016 axxx, 542 pages :billustrations ;c26 cm. atextbtxt2rdacontent aunmediatedbn2rdamedia avolumebnc2rdacarrier1 aTexts in applied mathematics,x0939-2475 ;vv. 65 aIncludes references and index. aIncludes bibliographical references and index.0 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. 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).--cSource other than Library of Congress. 0aDifferential equations. 7aDifferential equations.2fast0(OCoLC)fst008934461 aCain, John W.c(Mathematician),eauthor. 0aTexts in applied mathematics ;vv. 65. 31850-9999uhttp://link.springer.com/ 2lcccFR c11630d11630 00102lcc40708NFICaURSRODbURSRODcREFd2018-12-06l0oQA 371 Sch136 2016pURSROD-4526r2018-12-06w2018-12-06yFR