- I don't remember the differential coordinates and have to rely on derivation each time (for some reason the expressions aren't memorized yet because derivations are so much more reliable than memorizing the damn expression) - I've noticed that I get confused very often finding the expression for differential volume in spherical coordinates, so I am adding this visual to help me out: ![[sphericaldv.png]] - Also, this is in electrodynamics because this is where I used multivar calc the most. It's what helped me git gud at multivar calc. Do more electrodynamics ### Divergence theorem "Volume integral of the divergence of any vector over volume V equals total outward flux of that vector through surface S enclosing V" $\int{\nabla . \vec{D} \ dV} = \oint{\vec{D} . \vec{dS}}$ I don't know about you guys but this did not come to me intuitively. So let's ask ChatGPT. ### Conservative fields - Vector field whose line integral along any closed path is zero is called a conservative field - $\nabla \times \vec{V} = 0$