- #1

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Also, look those implicit equations: ##F(x, y(x))=0##, ##F(t, \vec{r}(t))=0##, ##F(x, y(x), y'(x), y''(x))=0##, ##F(t, \vec{r}(t), \vec{r}'(t))=0##... Can be understood that ##F## is the functional?

- Thread starter Jhenrique
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- #1

- 685

- 4

Also, look those implicit equations: ##F(x, y(x))=0##, ##F(t, \vec{r}(t))=0##, ##F(x, y(x), y'(x), y''(x))=0##, ##F(t, \vec{r}(t), \vec{r}'(t))=0##... Can be understood that ##F## is the functional?

- #2

Matterwave

Science Advisor

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It might be easier to explain with an example. Given a composite function ##g(f(t))## in order to return a number, we need to specify the value of ##t##. In other words ##g(f(2))## is a number while ##g(f(1))## is (potentially) a different number. Given a functional ##F[f(t)]## we need to specify the whole function ##f(t)## to give a number. In other words ##F[f(t)]## is already 1 number.

As for your follow up question. Those are usually functionals, yes, but where ambiguity might exist, the text should be clear about whether the object is a functional or a function. After all seeing ##F(f(t))## can be ambiguous. Often, texts will use square brackets to denote functionals (like I used above).

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