An applied course in ordinary differential equations. Students will develop the ability to describe physical situations with one or more differential equations. Students will learn to employ various solution techniques and analyze the properties of ordinary differential equations, including cases where explicit analytical solutions are not available. Students will become proficient in concepts and theory related to ordinary differential equations. Topics include, first order ordinary differential equations: direction fields, integrating factors, separable equations, homogeneous equations, autonomous equations, modelling, Euler's method, the existence and uniqueness theorem; higher order equations: constant coefficient equations, reduction of order, method of undetermined coefficients, variation of parameters, resonance; first order linear systems: eigenvalue method, classification, and non-homogeneous systems; non-linear equations: phase plane analysis and stability. Applications in life and physical sciences and economics.