Consider a surface S on which a scalar field f is defined

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"Consider a surface S on which a scalar field f is defined"

"Consider a surface S on which a scalar field f is defined"

what does "on which is defined" mean

phys descript answers appreciated!
 
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"Consider a surface S on which a scalar field f is defined"

"Consider a surface S on which a scalar field f is defined"

what does "on which is defined" mean

phys descript answers appreciated!
 
Suppose I have a surface parametrized by (x,y). Then I have a scalar field f(x,y), for example f(x,y) = x + y. Then I have a surface S on which a scalar field f is defined. For example defining the temperature at every point on a sphere.
 
It means there is a function defined which, to every point of the surface, assigns a scalar (number).
 
Double post! I am going to combine the two.
 
thanks
 

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