Welcome to my course, Differential Equations for Engineers. In this video, let me give you a broad overview. The course consists of six weeks, and we'll cover first order ODEs in week one, second order ODEs in weeks two, three and four, systems of ODEs in week five. And a taste of partial differential equations, or PDEs in week six. In the first week, I'll show you how to solve separate ball and linear first order odes. We'll look at some applications where I'll show you how to construct some basic differential equation models. In the second week, we'll study second order linear homogeneous differential equations. This includes the theoretical results of the principle of superposition and the Wronskian as well as the solution of the ode with constant coefficient. These equations correspond to unforced oscillations. In the third week, we'll learn about inhomogeneous differential equations, where the inhomogeneous terms can be exponential, sine or cosine, or polynomials. These equations correspond to forced oscillations. We'll also look at some applications including the RLC electrical circuit, a mass on a spring and the pendulum. The important phenomena of resonance will also be covered. In the fourth week, I'll teach the Laplace transform, and series solution methods. These are somewhat more sophisticated techniques. I'll define the Laplace transform, and discuss discontinuous and impulsive forces Forces using the Heaviside step function, and the Dirac delta function. We'll then solve the Airy's equation, a non-constant coefficient ode using the series solution method. In the fifth week, we'll learn how to solve a system of linear differential equations as a matrix eigenvalue problem. We'll see how to draw a phase portraits of the solution and learn about the important problem of normal modes, where seemingly complex oscillations can be understood as a linear superposition of more basic motions. In the sixth and final week, we'll study partial differential equations, we'll learn about Fourier series and solve the diffusion equation using the method of separation of variables. My course is composed of short lectures, practice problems, practice quizzes, and the graded quiz at the end of each week. If you can score better than 60% on all the graded quizzes, then you will be eligible to receive a course certificate. Thank you for joining me in this learning adventure of differential equations for engineers.