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Texts in Applied Mathematics

Ordinary Differential Equations: Basics and Beyond

Authors: Schaeffer, David, Cain, John Wesley

  • 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
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eBook $54.99
price for USA (gross)
  • ISBN 978-1-4939-6389-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for USA
  • ISBN 978-1-4939-6387-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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 (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).

About the authors

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.

Table of contents (10 chapters)

  • Introduction

    Schaeffer, David G. (et al.)

    Pages 1-39

  • Linear Systems with Constant Coefficients

    Schaeffer, David G. (et al.)

    Pages 41-78

  • Nonlinear Systems: Local Theory

    Schaeffer, David G. (et al.)

    Pages 79-109

  • Nonlinear Systems: Global Theory

    Schaeffer, David G. (et al.)

    Pages 111-160

  • Nondimensionalization and Scaling

    Schaeffer, David G. (et al.)

    Pages 161-194

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-1-4939-6389-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for USA
  • ISBN 978-1-4939-6387-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Ordinary Differential Equations: Basics and Beyond
Authors
Series Title
Texts in Applied Mathematics
Series Volume
65
Copyright
2016
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4939-6389-8
DOI
10.1007/978-1-4939-6389-8
Hardcover ISBN
978-1-4939-6387-4
Series ISSN
0939-2475
Edition Number
1
Number of Pages
XXX, 542
Number of Illustrations and Tables
78 b/w illustrations, 61 illustrations in colour
Topics