微分形式与楔积

What actually gets integrated

The wedge product

Computing with wedges

Forms as the course's unifying dictionary

Which object is the two-form $3x\, dx \wedge dy + y^2\, dx \wedge dz$ built to integrate over?

Simplify the wedge product $(y\, dx) \wedge (x\, dy)$ of these two one-forms.

The two-form $dx \wedge dy$ is integrated over the unit square. What value does the traversal orientation determine?

Give the coefficient of $dx \wedge dy$ in $(2\, dx) \wedge (3\, dy)$, as a plain number.

In three variables, give the highest degree a nonzero form can have, as a plain number.