A functional is a real-valued function on a vector space 
, usually of functions. For example,
the energy functional on the unit
disk 
assigns a number to any differentiable function 
,
 |
For the functional to be continuous, it is necessary for the vector space 
of functions to have an appropriate topology. The widespread
use of functionals in applications, such as the calculus
of variations, gave rise to functional analysis.
The reason the term "functional" is used is because 
can be a space of functions, e.g.,
![V={f:[0,1]->R:f is continuous}](/images/equations/Functional/NumberedEquation2.svg) |
in which case 
is a linear functional on 
.
