ABSTRACT
In order to facilitate the development and cataloguing of the variety of theorems describing the transformation of derivatives from one scale to another, a consistent and convenient notational scheme is employed. Within this nomenclature scheme, two important classes of theorems are of particular interest: 1) integration theorems that involve only microscopic and megascopic scales, and 2) averaging theorems that always involve microscopic and macroscopic scales but may also involve the megascopic scale. The starting point for both classes of theorems is the integration of the derivative of a function describing microscale behavior. Through this integration, the function is transformed to either the macroscale, the megascale, or some mix of the two scales. Furthermore, if the transformation is to the macroscale, the spatial derivatives are also transformed to that scale.
