This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner.

Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations.

Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.

Viorel Barbu is Professor of Mathematics at the Alexandru Ioan Cuza University of Iasi, Romania, and member of the Romanian Academy and the European Academy of Sciences. He is the author of several monographs and textbooks on partial differential equations, optimal control, nonlinear analysis, and optimization theory.

Introduction.- Existence and uniqueness for the Cauchy problem.- Systems of linear differential equations.- Stability theory.- Prime integrals and first-order partial differential equations.