Leading-order term

The leading-order terms (or leading-order corrections) within a <a href="/facts/Mathematics/pxTouaz4">mathematical</a> <a href="/facts/Equation/pxFzLAVR">equation</a>, <a href="/facts/Expression_(mathematics)/MPrMlYbE">expression</a> or <a href="/facts/Mathematical_model/CGhyuxgz">model</a> are the <a href="/facts/Term_(logic)/M0nXp7dH">terms</a> with the largest <a href="/facts/Order_of_magnitude/cWzRP2dM">order of magnitude</a>. The sizes of the different terms in the equation(s) will change as the <a href="/facts/Variable_(mathematics)/VbQlrvKz">variables</a> change, and hence, which terms are leading-order may also change.
A common and powerful way of simplifying and understanding a wide variety of complicated mathematical models is to investigate which terms are the largest (and therefore most important), for particular sizes of the variables and parameters, and analyse the behaviour produced by just these terms (regarding the other smaller terms as negligible). This gives the main behaviour – the true behaviour is only small deviations away from this. 
The main behaviour may be captured sufficiently well by just the strictly leading-order terms, or it may be decided that slightly smaller terms should also be included. In which case, the phrase "leading-order terms" might be used informally to mean this whole group of terms. The behaviour produced by just the group of leading-order terms is called the leading-order behaviour of the model.

Leading-order term open-in-new

Leading-order term