Discovering The Laplace Transform in Undergraduate Differential Equations

The Laplace Transform is one of the most powerful mathematical tools that can be used to solve a wide variety of problems in Math, Science, and Engineering. We begin this course by discussing what the Laplace Transform is and why it is important. Next, we show the Laplace Integral, and derive several fundamental transformations that we will use in the remainder of the course. We also discuss the Inverse Laplace Transform and derive several inverses. We discuss how to solve Ordinary Differential Equations (ODEs) with initial conditions and work several examples to give practice with real problems.

The Laplace Transform is one of the most powerful mathematical tools that can be used to solve a wide variety of problems in Math, Science, and Engineering. We begin this course by discussing what the Laplace Transform is and why it is important. Next, we show the Laplace Integral, and derive several fundamental transformations that we will use in the remainder of the course. We also discuss the Inverse Laplace Transform and derive several inverses. We discuss how to solve Ordinary Differential Equations (ODEs) with initial conditions and work several examples to give practice with real problems. Finally, we discuss the shifting properties of the Laplace Transform and how to work with piecewise defined functions.