This textbook takes a modeling and computing approach to updating the Elementary or Ordinary Differential Equations Course. The age of computing is upon us and we need to develop new courses and methods for teaching differential equations. This textbook is an attempt to facilitate some changes. It is designed for instructors who wish to bring the computer into the classroom and emphasize and integrate the use of computers in the teaching of differential equations. Many examples and exercises require the use of some computer software to solve a problem.