Calculus

Where this has got to

Calculus is the mathematics of quantities that are changing while you measure them. Everything in it is a rate or a total: how steep, how fast, how much has accumulated so far. Both of those run into the same obstacle straight away. A rate needs two measurements and the difference between them, so a rate at a single instant has no second measurement to work with, and every real instrument returns an average over a gap rather than a value at a point. One construction gets around that, and the whole subject is built on it and on nothing else. This subject is one page deep. That page takes two points on a curve, slides them together, watches the arithmetic collapse to 0/0 while the picture keeps a perfectly good answer, and builds the limit that resolves it. It stops one step short of naming what the settled slope is called. That name, its notation and the rules for computing it are the derivative, which is the next page and is not built yet. Saying so is more use than a list of chapters that link nowhere.