Total increment
From Encyclopedia of Mathematics
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
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