Nebla is ubiquitous in mathematics; the Nabla dot and Nabla cross product are concepts we learn in middle school, but revisiting them today through the lens of differential forms opens up a new door and provides a fresh perspective that’s truly mind-opening.

calculus is quite limited and going further could be confusing, for example when asked to do ∇∇f,

If we translate to differential form language,

the d*w is relatively new for me, but we know $d$d increases the form degree by 1, d∗ decreases the form degree by 1; For a 1-form (vector field), $d^*$d∗ gives the divergence scalar. the below is bit of gibberish, but may get more clear later on