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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).
Differential equations arise in a variety of contexts, some purely
theoretical and some of practical interest. As you read this
textbook, you will find that the qualitative and quantitative study
of differential equations incorporates an elegant blend of linear
algebra and advanced calculus. This book is intended for an
advanced undergraduate course in differential equations. The reader
should have already completed courses in linear algebra,
multivariable calculus, and introductory differential equations.
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