ABSTRACT
The concept of a transform is that it turns a given function into another function. This chapter discusses the use of Laplace transforms to the applications of differential equations. The Laplace transform changes solving a differential equation from a rather complicated calculus problem to a simple algebra problem. The only thing that remains, in order to find an explicit solution to the original differential equation with initial conditions, is to find the inverse Laplace transform of the equation. The chapter looks at the derivatives and integrals of Laplace transforms, and summarizes the chief properties of the Laplace transform in a table. It explains convolutions; the convolution formula is particularly useful in calculating inverse Laplace transforms.
