Ordinary Differential Equations: Basics And Beyond (texts In Applied Mathematics)
by David G. Schaeffer /
2016 / English / EPUB
6.2 MB Download
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.
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).
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).
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).
