Functionals

A functional is a special type of mathematical rule that takes a function as input and produces a single number as output. Think of it like a machine where you input a entire function (which describes a relationship or a process), and the machine calculates a number that summarizes some aspect of that function—for example, its average value, total energy, or maximum height. Functional is a key concept in advanced mathematics and physics, used to analyze and understand how entire functions behave, often in areas like calculus, differential equations, and quantum mechanics.