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Total increment

From Encyclopedia of Mathematics
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of a function of several variables

The increment acquired by the function when all the arguments undergo, in general non-zero, increments. More precisely, let a function be defined in a neighbourhood of the point in the -dimensional space of the variables . The increment

of the function at , where

is called the total increment if it is considered as a function of the possible increments of the arguments , which are subject only to the condition that the point belongs to the domain of definition of . Along with the total increment of the function, one can consider the partial increments of at a point with respect to the variable , i.e. increments for which , , and is fixed .

How to Cite This Entry:
Total increment. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Total_increment&oldid=49002
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article