This course is about differential equations, and covers material that all engineers should know. We will learn how to solve first-order equations, and how to solve second-order equations with constant coefficients and also look at some fundamental engineering applications. We will learn about the Laplace transform and series solution methods. Finally, we will learn about systems of linear differential equations, including the very important normal modes problem, and how to solve a partial differential equation using separation of variables. This solution method requires first learning about Fourier series. After each video, there are problems to solve and I have tried to choose problems that exemplify the main idea of the lecture. I try to give enough problems for students to solidify their understanding of the material, but not so many that students feel overwhelmed. I do encourage students to attempt the given problems, but if they get stuck, full solutions can be found in the lecture notes for the course. Lecture notes may be downloaded at http://www.math.ust.hk/~machas/differential-equations-for-engineers.pdf