I want to ask that why $Φ(x,y,z) = x^3y - z^2$. I don't understand this relation? Can someone make sense of this equation.
closed as not a real question by Manishearth♦ Jan 29 at 4:16
It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, see the FAQ.
The right hand side of your equation represents a "scalar field" in space. A scalar field is a function that has a number corresponding to each point in space.
If the x,y and z coordinates of a particular point in space is (1,2,3), then the number corresponding to that point in space, for the scalar field in your equation, is $x^3y - z^2 = 1^3*2 - 3^3 = -7$. That is, you simply substitute the coordinates of a particular point in space into the equation, and you arrive at the number corresponding to that point.
When are scalar fields used in real life? A simple example of a scalar field is temperature. That is, each point in space might have a particular temperature.