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Ordinary differential equationsbasic...

Cain, John W.

Ordinary differential equationsbasics and beyond /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Ordinary differential equationsby David G. Schaeffer, John W. Cain.
其他題名:	basics and beyond /
作者:	Schaeffer, David G.
其他作者:	Cain, John W.
出版者:	New York, NY :Springer New York :2016.
面頁冊數:	xxx, 542 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
標題:	Differential equations.
電子資源:	http://dx.doi.org/10.1007/978-1-4939-6389-8
ISBN:	9781493963898$q(electronic bk.)

Ordinary differential equationsbasics and beyond /
Schaeffer, David G.

Ordinary differential equationsbasics and beyond /[electronic resource] :by David G. Schaeffer, John W. Cain. - New York, NY :Springer New York :2016. - xxx, 542 p. :ill. (some col.), digital ;24 cm. - Texts in applied mathematics,v.650939-2475 ;. - Texts in applied mathematics ;40..

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.

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 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)

ISBN: 9781493963898$q(electronic bk.)

Standard No.: 10.1007/978-1-4939-6389-8doiSubjects--Topical Terms:

183925
Differential equations.

LC Class. No.: QA371

Dewey Class. No.: 515.352

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505 0 $a 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.
520 $a 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 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)
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