This is an applied course in ordinary differential equations, which is primarily for students in the physical, behavioral and engineering sciences. Differential equations are the fundamental tools that modern science and engineering use to model physical reality. This course consists of concepts generally encountered in a first course in differential equations including a comprehensive treatment of first order differential equations employing a variety of solution techniques. A study of higher order equations, largely second order, is included with emphasis on linear equations possessing constant coefficients as well as variable coefficients. Classical and contemporary applications are included throughout coming from diverse fields such as mechanics, electrical circuits, economics and concludes with a discussion of the Laplace transform and its application to linear equations with constant coefficients.