14. The Function Calculus and Complex-Valued Carriers (R12)
The product / quotient / reciprocal calculus covers the algebraic defining relations of the ISQ (area is length times length, speed is length over duration). Scientific models do two further things the algebra alone does not reach: they apply functions to quantities (roots, exponentials, logarithms, the trigonometric functions), and they take complex values (the relative permittivity of a lossy dielectric, an impedance, a phasor). This chapter adds the two carrier-level extensions that cover both — the function calculus (a carrier capability, plus kind-relations for functions) and the complex carrier (a carrier construction) — and the point of each is that the kind layer is left untouched: only what a magnitude can do, or what numbers it lives in, changes.