In this lecture I introduce differential forms, which are completely antisymmetric smooth covariant tensor fields. I define the exterior of wedge product, and discuss its properties. I finish with an example of our familiar 3 dimensional space and show that here the wedge product is connected to the familiar products from vector algebra - the dot and the cross product.
![](https://i.ytimg.com/vi/3M9wzv1EhtI/maxresdefault.jpg)