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).
