Meaning of LINEAR APPROXIMATION in English

LINEAR APPROXIMATION

In mathematics, the process of finding a straight line that closely fits a curve ( function ) at some location.

Expressed as the linear equation y = a x + b , the values of a and b are chosen so that the line meets the curve at the chosen location, or value of x , and the slope of the line equals the rate of change of the curve ( derivative of the function) at that location. For most curves, linear approximations are good only very close to the chosen x . Yet much of the theory of calculus , including the fundamental theorem of calculus and the mean-value theorem for derivatives, is based on such approximations.

Britannica English dictionary.      Английский словарь Британика.