An Intro to Differential Forms
Differential forms are powerful tools, but a lot of the geometric intuition is hidden behind the formalism. Let’s fix that.
With the exception of The Charged Particle Lagrangian, we’ve done little to no Vector Calculus. Sure we’ve talked about a few operators from Vector Calculus, but we’ve pulled formulas and identities out of thin air with no explanation. Over the next few articles, we’re going to fix that problem.
To do so, we’re going to introduce the concept of a differential form. Differential forms give us one unified approach to Vector Calculus and Integration in arbitrary coordinates. We’ll be able to derive several important theorems and rewrite Maxwell’s Equations in ways that are more practical in different situations. For this article, we’re going to talk about two of the core operators of Differential Forms: the wedge product ∧ and the Hodge star operator ⋆.
Check Your Understanding
This article can’t cover everything we would need to do all the cool stuff, so I only have a few questions for you.
Surface Area of a Sphere
Use a differential two-form to find the surface area of a sphere by finding the…
