This short-but-important supplemental lecture introduces some language we’ll need for describing geometry (curves, surfaces, etc.) in terms of differential forms. So far, we’ve said that a differential -form produces a scalar measurement. But when talking about geometry, we often care about quantities that are vector-valued rather than scalar-valued. For instance, positions in , tangents, and normals are all vector-valued quantities. For the most part, all of our operations look pretty much the same as before. The one exception is the wedge product, which in we now define in terms of the cross product.
