English

The Specular Derivative

Classical Analysis and ODEs 2025-12-30 v2

Abstract

In this paper, we introduce a new generalized derivative, which we term the specular derivative. We establish the Quasi-Rolles' Theorem, the Quasi-Mean Value Theorem, and the Fundamental Theorem of Calculus in light of the specular derivative. We also investigate various analytic and geometric properties of specular derivatives and apply these properties to several differential equations.

Keywords

Cite

@article{arxiv.2210.06062,
  title  = {The Specular Derivative},
  author = {Kiyuob Jung and Jehan Oh},
  journal= {arXiv preprint arXiv:2210.06062},
  year   = {2025}
}

Comments

34 pages, 11 figures

R2 v1 2026-06-28T03:25:21.243Z