Fundamental Theorem of Calculus

TL;DR

This paper provides a rigorous geometric calculus proof of the Fundamental Theorem of Calculus, discusses classical theorems like Green's and Stokes', and introduces the concept of monogenic functions as a higher-dimensional generalization of analytic functions.

Contribution

It offers a new geometric calculus proof of the Fundamental Theorem of Calculus and extends the concept of analytic functions to higher dimensions through monogenic functions.

Findings

Geometric calculus provides a rigorous proof of the Fundamental Theorem of Calculus.

Classical theorems like Green's and Stokes' are discussed within this framework.

Introduction of monogenic functions as a higher-dimensional generalization of analytic functions.

Abstract

A simple but rigorous proof of the Fundamental Theorem of Calculus is given in geometric calculus, after the basis for this theory in geometric algebra has been explained. Various classical examples of this theorem, such as the Green's and Stokes' theorem are discussed, as well as the new theory of monogenic functions, which generalizes the concept of an analytic function of a complex variable to higher dimensions.