Differential equations are of fundamental importance in the applications of mathematics to the physical and biological sciences. This text provides an elementary but cohesive development of the topic. The primary goal of the book is to teach students how to use differential equations in applied areas. To this end, the book includes more than 400 worked examples and 2500 exercises, chapter summaries than include a review of the important concepts, chapter review exercises, self-quiz problems, numerous applications in various fields, a section in each chapter on solving problems using symbolic manipulators such as Mathematica, MAPLE, and DERIVE, and a manual for such solutions.