Introduction to Semi-discrete Calculus

TL;DR

This paper introduces Semi-discrete Calculus, a new mathematical framework for analyzing local trends in functions, complementing traditional infinitesimal calculus methods like derivatives and integrals.

Contribution

It proposes a novel framework for studying functions' local trends, expanding the tools available beyond classical infinitesimal calculus.

Findings

Semi-discrete Calculus effectively models local trends.

It provides a new perspective for analyzing change.

The framework is applicable across sciences and engineering.

Abstract

The Infinitesimal Calculus explores mainly two measurements: the instantaneous rates of change and the accumulation of quantities. This work shows that scientists, engineers, mathematicians, and teachers increasingly apply another change measurements tool: functions' local trends. While it seems to be a special case of the rate (via the derivative sign), this work proposes a separate and favorable mathematical framework for the trend, called Semi-discrete Calculus.