Function question (split from Ordinary differential equation)

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I need someone to tell me what u(.,t) means when u is a function of x and t. x is in Rn

Edited by Niyilium
Incomplete

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It means the function defined on $$\mathbb{R}^n$$ that maps $$x$$ to $$u(x,t).$$

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For example, if u(x, t)= x2+ t2 then u(., t) is the function that takes 3 to the function u(3, t)= 9+ t2, that takes 5 to u(5, t)= 25+ t2, etc.  It maps a number to a function.

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Is this the same as currying? (I have never seen this notation before .... )

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1 hour ago, HallsofIvy said:

For example, if u(x, t)= x2+ t2 then u(., t) is the function that takes 3 to the function u(3, t)= 9+ t2, that takes 5 to u(5, t)= 25+ t2, etc.  It maps a number to a function.

This is not an example of what I wrote . It also makes sense, but I cannot recall having seen it before.

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