This book is intended to be an introduction to Delay Differential Equations for upper level undergraduates or beginning graduate mathematics students who have a reasonable background in ordinary differential equations and who would like to get to the applications quickly.
The author has used preliminary notes in teaching such a course at Arizona State University over the past two years.
This book focuses on the key tools necessary to understand the applications literature involving delay equations and to construct and analyze mathematical models involving delay differential equations. The book begins with a survey of mathematical models involving delay equations.

Hal Smith is a Professor at the School of Mathematical and Statistical Sciences at Arizona State University.

1 Introduction.-The Simplest Delay Equation.-Delayed Negative Feedback: A Warm-Up.- Existence of Solutions.- Linear Systems and Linearization.- Semidynamical Systems and Delay Equations.- Hopf Bifurcation.- Distributed Delay Equations and the Linear Chain Trick.- Phage and Bacteria in a Chemostat.-References.- Index.