The word differential has several related meanings in mathematics. In the most common context, it means "related to derivatives." So, for example, the portion of calculus dealing with taking derivatives (i.e., differentiation), is known as differential calculus.
For a differentiable function 
, let 
denote a change in 
. The differential of 
is
 |
The differential is the linear part of the change 
, so 
is the linear approximation
to 
for small 
. The differential 
is the one-form whose value
on the increment 
is 
.
