**Plenary Lecture
On the Tensorial Properties of Derivatives**

**Professor Gregory L. Light**

Department of Finance

Providence College (PC)

Rhode Island, USA

E-mail: GLIGHT@providence.edu

**Abstract: ** The operation of differentiation is relative to a particular spacetime frame in physics and is otherwise specific to any incidental set of units, with changes in frames or units succinctly treated as the pull-back homomorphism in differential topology, based on which my talk will address, e.g., the Weyl gauge invariance, implicit function theorem, perturbation analyses and dynamical systems. Newton and Leibniz introduced derivative dy/dx around 1670; Cournot mod- ified it into "elasticity" (dy/dx)(x/y) around 1838; we integrate the two as "rel- ative derivative" (dy/dx)(a/b), with a, b = any expediently chosen constants. While (dy/dx)(x/y) = (d lny)/(d lnx) suffers from analytical limitations, our relative derivative has the advantage of being a differential 1-form executing ex- terior differentiation. As such, one can make quantitative predictions on dy/b = (dy/dx)(a/b) (dx/a) with the relative derivative simulated by plausible values from any professional insights, rather than qualitatively examining the signs in dy = (dy/dx) dx. In this way, we advance applications of derivatives to all fields that do not possess distinct sets of units as physics does.

**Brief Biography of the Speaker: ** Dr. Gregory L. Light is Professor of Finance of Providence College (PC), where he has been teaching Statistics, Operations Research, among other quantitative subjects. Passionate in his subjects and caring for his students, he was nominated for the 2005 - 2006 Joseph R. Accinno Faculty Teaching Award by the PC Students Congress and more recently in 2015 awarded for teaching innovation. Equally engaged in has been his collaborative scholarly activities with his colleagues, opening new research avenues mutually. Dr. Light received his B.A. in Economics from National Taiwan University, M.B.A. from University of Illinois, Ph.D. in Business Economics and Public Policy from University of Michigan, followed by an M.A. in Mathematics by staying at UM-Ann Arbor and then a Ph.D.-ABD in Dynamical Systems in Applied Mathematics from Brown University. The dual tracks of his pursuits evolved from his interests in Mathematical Economics, Dynamical Systems and Physics. In Economics, he has proposed the analytic methodology of “relative derivatives” as an integration of elasticities in Economics with derivatives in Mathematics. In Physics, he published, Quantum Particle-Waves in a Combined Universe by General Relativity, Scholars’ Press, Saarbrucken, Germany, 2016, and gave a WSEAS Plenary Speech, “Pauli Matrices and Quantum Information,” in the 21st International Conference on Applied Mathematics (AMATH '16), Bern, Switzerland, December 17-19, 2016. He plans to continue his interest in mathematical modeling, extending his research and enriching his teaching.