Differential Calculus of Zeon Functions

• DOI: 10.1007/s00006-019-0943-6
• Publication Date: 2019-02-08T01:05:26Z
• Authors: G. Stacey Staples
• Keywords: Differential calculus; Time-scale calculus; Calculus of variations

Analogous to real functions, zeon functions are defined as zeon-valued functions of a zeon variable. In this paper, formal criteria for continuity and differentiability of zeon functions are put on a rigorous footing and the “usual” differentiation rules are formally established. As special cases, zeon extensions of real functions and zeon functions of one real variable are considered.