# A simple and more general approach to Stokes' theorem

## TL;DR

This paper proposes a simpler, more general method for deriving Stokes' theorem that avoids complex invariance and boundary orientation concepts, making it more accessible and rigorous.

## Contribution

It introduces a novel approach to Stokes' theorem that simplifies its derivation and broadens its applicability compared to traditional methods.

## Key findings

- Provides a more accessible derivation of Stokes' theorem
- Eliminates the need for invariance of curl under transformations
- Offers a rigorous definition of boundary orientation

## Abstract

Oftentimes, Stokes' theorem is derived by using, more or less explicitly, the invariance of the curl of the vector field with respect to translations and rotations. However, this invariance -- which is oftentimes described as the curl being a "physical" vector -- does not seem quite easy to verify, especially for undergraduate students. An even bigger problem with Stokes' theorem is to rigorously define such notions as ``the boundary curve remains to the left of the surface''. Here an apparently simpler and more general approach is suggested.