i was never very good at pie in the sky math.
Its was only when engineering showed me what it was good for that it became obvious.
Calculus works out the area under a graph, we use it for loadings on a beam working out energy in a system. And also allows you to pull data from individual points inrespect to other variables. eg you have a graph showing the distance travelled down a runway along with the time you can work out the speed, the accel at any point you like.
laplace is used for control but you can use it for pretty much everything if it takes your fancy.
And pug you have missed out a dimension in your spherical