[p_j_w]

>I could have used this 32(!) years ago when I was struggling in college.

I was struggling with this material more like 15 years ago, but same. I wish someone had explained the LaPlacian like this when I was in Multivariable calculus:

>Find me a function f where every value everywhere is the average of the values around it.

It's so simple and easy to grasp, yet provides so much insight into what's going on when you're doing the actual calculation behind the operation, but is so easy to lose sight of when you're overwhelmed with figuring out the 'mechanics' of it and everything else that was covered in the day's lesson plan.