Ordinary Differential Equations: Basics an...

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Beschreibung

This 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 thetext ([...]

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).

Über den Autor

David G. Schaeffer is Professor of Mathematics at Duke University. His research interests include partial differential equations and granular flow.

John W. Cain is Professor of Mathematics at Harvard University. His background is in application-oriented mathematics with interest in applications to medicine, biology, and biochemistry.

Zusammenfassung

Includes ample commentary on exercises to help explain their significance and provide a deeper understanding of content

Detailed appendices gives readers self-study opportunities

Supports practical uses of subject matter and broader scientific awareness

Includes supplementary material: [...]

Inhaltsverzeichnis

Introduction.- 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.

Details

Erscheinungsjahr:	2016
Fachbereich:	Analysis
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xxx 542 S. 78 s/w Illustr. 61 farbige Illustr. 542 p. 139 illus. 61 illus. in color.
ISBN-13:	9781493963874
ISBN-10:	1493963872
Sprache:	Englisch
Einband:	Gebunden
Autor:	Cain, John W. Schaeffer, David G.
Auflage:	1st edition 2016
Hersteller:	Springer US Springer New York
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	260 x 183 x 37 mm
Von/Mit:	John W. Cain (u. a.)
Erscheinungsdatum:	12.11.2016
Gewicht:	1,259 kg

Artikel-ID: 107930989