# k-Chains and k-Cells

13 min readApr 1, 2023

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

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…