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Orders of approximation
In science, engineering, and other quantitative disciplines, orders of approximation refer to formal or informal terms for how precise an approximation is, and to indicate progressively more refined approximations: in increasing order of precision, a zeroth-order approximation, a first-order approximation, a second-order approximation, and so forth.
Formally, an ''n''th-order approximation is one where the order of magnitude of the error is at most , or in terms of big O notation, the error is
In suitable circumstances, approximating a function by a Taylor polynomial of degree ''n'' yields an ''n''th-order approximation, by Taylor's theorem: a first-order approximation is a linear approximation, and so forth.
The term is also used more loosely, as detailed below.
==Usage in science and engineering==
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