Welcome to Differential
Equations for Engineers. In this video, let me give you a broad overview of the course. The course consists of six weeks, and we'll cover first-order
ODEs in Week 1, second-order ODEs in
Weeks 2 through 4, systems of ODEs in Week 5, and a taste of partial
differential equations in Week 6. In the first week, we'll solve separable and
linear first-order ODEs, and construct some basic
differential equation models. In the second week, we'll solve second-order linear homogeneous
differential equations. We'll learn about
the principle of superposition and the Wronskian, and how to solve ODEs with
constant coefficients. In the third week, we'll solve inhomogeneous
differential equations, where the inhomogeneous
terms can be exponential, sine or cosine, or polynomials. Applications will include
the RLC electrical circuit, a mass on a spring,
and a pendulum. We'll also study resonance. In the fourth week, we'll study the Laplace transform and series
solution methods. We'll define the
Laplace transform, and discuss discontinuous
and impulsive 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 solve a system of linear differential equations as a matrix eigenvalue problem. We'll draw a phase
portraits of the solution, and learn about the important
problem of normal modes. 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 a graded quiz at
the end of each week. If you can score better than 60 percent on all
the graded quizzes, then you'll be eligible to
receive a course certificate. Thank you for joining me
in this learning adventure of differential
equations for engineers.