any proper aengineer has a heavy toolbelt on them at all times, brimming with magick instruments that let them break down even the stickiest problems. in this section, we'll analyze our current tools for function analysis and beef them up, then add a couple new ones!
a quick overview: first, we'll take a look at our "present" finding operation, and see if it really can handle every case we need (spoiler: it doesn't). then we'll talk about our inputs and outputs- how do we manage them if they're rowdy? finally, we'll get to a very exciting discussion: new dimensions!
these tools form a nice foundation that we'll start to build our exquisite structure of hypercalculus/ function analysis/ differential geometry/ "whatever you want to call it, we're just making things into lines" on!