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Ordinary Differential Equations: Basics and Beyond de David G. Schaeffer

Ordinary Differential Equations: Basics and Beyond: Texts in Applied Mathematics, cartea 65

Autor David G. Schaeffer, John W. Cain
en Limba Engleză Hardback – 12 noi 2016
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 (www.math.duke.edu/ode-book). 

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).

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Specificații

ISBN-13: 9781493963874
ISBN-10: 1493963872
Pagini: 537
Ilustrații: XXX, 542 p. 139 illus., 61 illus. in color.
Dimensiuni: 178 x 254 x 37 mm
Greutate: 1.26 kg
Ediția:1st ed. 2016
Editura: Springer
Colecția Springer
Seria Texts in Applied Mathematics

Locul publicării:New York, NY, United States

Cuprins

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.

Notă biografică

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.

Textul de pe ultima copertă

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 supportingthe 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).

Caracteristici

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: sn.pub/extras