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). Β While proofs are rigorous, the exposition is reader-friendly, aiming for the informality of face-to-face interactions.Β
A unique feature of this book is the integration of rigorous theory with numerous applications of scientific interest. Β Besides providing motivation, this synthesis clarifies the theory and enhances scientific literacy. Other features include: Β (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).Β
Given its many applications, the book may be used comfortably in science and engineering courses as well as in mathematics courses. Β 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).