Our next lecture will cover one of the basic tools we’ll use throughout the rest of the course: exterior algebra. The basic idea is to add a couple new operations to our usual list of vector operations (dot product, cross product, etc.) that make it easy to talk about volumes rather than just vectors. If you felt ok working with things like the cross product and the determinant in your linear algebra/vector calculus courses, this shouldn’t be too big of a leap. (If not, could be a good moment for a review!)
On slide 44/1 hour in, $\star(3v_1 \wedge v_2 \wedge v_3)$ should be 1/3 instead of 3 right?
I don’t think so; $\star(e_1 \wedge e_2 \wedge e_2) = 1$, so $\star(3e_1 \wedge e_2 \wedge e_2) = 3$.