## ABSTRACT

This chapter introduces the mathematical entities commonly known as “delta functions”. These are not really functions, at least not in the classical sense. Instead, they are simple examples of the class of “generalized functions”. Nonetheless, with a modicum of care, they can be treated like classical functions. More importantly, they are useful. They are valuable in modeling both “strong forces of brief duration” (such as the force of a baseball bat striking a ball) and “point masses”. Moreover, their mathematical properties turn out to be remarkable, making them some of the simplest “functions” to deal with.

The chapter begins with a ‘working’ definition for the delta functions, and a discussion of how these generalized functions model strong forces of brief duration and point masses. This naturally leads to another working definition involving the integration of the product of a delta function with a classical function, which, in turn, provides the integral property that makes the mathematics of delta functions so simple and elegant. The Laplace transforms of the delta functions are computed, and differential equations with delta functions as forcing functions are solved, providing further insight on Duhamel’s principle.