Ordinary Differential Equations: Basics and Beyond

  • David G. Schaeffer
  • John W. Cain

Part of the Texts in Applied Mathematics book series (TAM, volume 65)

Table of contents

  1. Front Matter
    Pages i-xxx
  2. David G. Schaeffer, John W. Cain
    Pages 1-39
  3. David G. Schaeffer, John W. Cain
    Pages 41-78
  4. David G. Schaeffer, John W. Cain
    Pages 79-109
  5. David G. Schaeffer, John W. Cain
    Pages 111-160
  6. David G. Schaeffer, John W. Cain
    Pages 161-194
  7. David G. Schaeffer, John W. Cain
    Pages 195-258
  8. David G. Schaeffer, John W. Cain
    Pages 259-325
  9. David G. Schaeffer, John W. Cain
    Pages 327-401
  10. David G. Schaeffer, John W. Cain
    Pages 403-450
  11. David G. Schaeffer, John W. Cain
    Pages 451-486
  12. Back Matter
    Pages 487-542

About this book

Introduction

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).

Keywords

Ordinary Differential Equations Dynamical Sysems Bifurcation Theory Linear Systems Nonlinear Systems

Authors and affiliations

  • David G. Schaeffer
    • 1
  • John W. Cain
    • 2
  1. 1.Department of MathematicsDuke UniversityDurhamUSA
  2. 2.Mathematics DepartmentHarvard UniversityCambridgeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-6389-8
  • Copyright Information Springer Science+Business Media New York 2016
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-6387-4
  • Online ISBN 978-1-4939-6389-8
  • Series Print ISSN 0939-2475
  • Series Online ISSN 2196-9949
  • About this book