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. This entry contributed by Todd Rowland. Rowland, Todd. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more.
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Ask Question. Asked 8 years, 8 months ago. Active 2 years ago. Viewed 26k times. I guess the difference is when we refer to functional we mean a set of possible functions; but when we say function we mean a specific function not a set of functions.
Show 1 more comment. Active Oldest Votes. Fried Brice Fried Brice 2 2 silver badges 5 5 bronze badges. I think most classical problems fall along similar lines, a function that eats functions and spits out scalars.
But I'm sure the word "functional" has been applied to the situation you're thinking of, e. Add a comment. Added: Ah, I also forgot that sometimes people call "functions of functions" functionals. Do look into the link to see if it adds more direction. Kirk Walla Kirk Walla 76 1 1 silver badge 4 4 bronze badges. Upcoming Events. Featured on Meta.
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