An accessible, practical introduction to the principles of
differential equations

The field of differential equations is a keystone of scientific
knowledge today, with broad applications in mathematics,
engineering, physics, and other scientific fields. Encompassing
both basic concepts and advanced results, Principles of
Differential Equations is the definitive, hands-on introduction
professionals and students need in order to gain a strong knowledge
base applicable to the many different subfields of differential
equations and dynamical systems.

Nelson Markley includes essential background from analysis and
linear algebra, in a unified approach to ordinary differential
equations that underscores how key theoretical ingredients
interconnect. Opening with basic existence and uniqueness results,
Principles of Differential Equations systematically illuminates the
theory, progressing through linear systems to stable manifolds and
bifurcation theory. Other vital topics covered include:

* Basic dynamical systems concepts

* Constant coefficients

* Stability

* The Poincaré return map

* Smooth vector fields

As a comprehensive resource with complete proofs and more than
200 exercises, Principles of Differential Equations is the ideal
self-study reference for professionals, and an effective
introduction and tutorial for students.