I'm reading a book on calculus, the part about vector fields on manifolds. It's a nice book, but with a severe drawback --- it has no pictures.
I like how vectors are treated algebraically, as derivatives over a local ring (ring of germs). But I still want to use "geometrical" view on vector fields.
The problem is I can't imagine vector field "multiplication" as a composition of derivatives. And thus I can't picture commutator of two vector fields.
Has anybody here got pictures too help me?