k-Chains and k-Cells

Joseph Mellor
13 min readApr 1, 2023

To prove the Generalized Stokes’ Theorem, we’ll some way of defining a region and its boundary.

This is stop 17 on The Road to Quantum Mechanics. I’m going to start trying to draw more for these articles and I’ve been working on a secret drawing app that I’ve used to make some of the artwork for this article.

We want to prove everything in Vector Calculus by introducing objects known as differential forms. Up to this point, we’ve derived a formula for the volume element and formulas for the gradient, divergence, curl, Laplacian, and vector Laplacian in arbitrary coordinate systems. We were also able to prove any identity in Vector

--

--

Joseph Mellor

BS in Physics, Math, and CS with a minor in High-Performance Computing. You can find all my articles at https://josephmellor.xyz/articles/.