Ordinary Differential Equations: Basics and Beyond

Authors: David G. Schaeffer, John W. Cain



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

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).

Table of contents

Front Matter
Pages i-xxx

Introduction
Pages 1-39

Linear Systems with Constant Coefficients
Pages 41-78

Nonlinear Systems: Local Theory
Pages 79-109

Nonlinear Systems: Global Theory
Pages 111-160

Nondimensionalization and Scaling
Pages 161-194

Trajectories Near Equilibria
Pages 195-258

Oscillations in ODEs
Pages 259-325

Bifurcation from Equilibria
Pages 327-401

Examples of Global Bifurcation
Pages 403-450

Epilogue
Pages 451-486

Back Matter
Pages 487-542

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