Introduction

Abstract

A differential form is simply this: an integrand. In other words, it is a thing which can be integrated over some (often complicated) domain. For example, consider the following integral: $\int\limits_0^1 {x^2 } dx$. This notation indicates that we are integrating x ² over the interval [0, 1]. In this case, x ² dx is a differential form. If you have had no exposure to this subject, this may make you a little uncomfortable. After all, in calculus we are taught that x ² is the integrand. The symbol “dx” is only there to delineate when the integrand has ended and what variable we are integrating with respect to. However, as an object in itself, we are not taught any meaning for “dx.” Is it a function? Is it an operator on functions? Some professors call it an “infinitesimal” quantity.