linearization
Replacing a nonlinear function near a chosen point by its tangent line — keeping only the constant and first-derivative terms of the Taylor expansion. Near `x = 0`, `sin x ≈ x`, `cos x ≈ 1 − x²/2`, `e^x ≈ 1 + x`. The approximation is excellent for small `|x|` and grows wrong as `|x|` increases. Mechanical clocks, electrical circuit analysis, control systems, and most of "the engineering equations" are linearized versions of much harder nonlinear ones, valid in the small-deviation regime where everything in the system is supposed to live.
1715 · Brook Taylor · London
Taylor's *Methodus Incrementorum* gave the series that bears his name — 'replace any function near a point by its tangent line, then by its tangent parabola, and so on'. Every linearization in physics, ML, and engineering is a one-term Taylor expansion.