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A 0-form on 3-space (x,y,z) is a smooth map f(x,y,z) of
3-space onto the real numbers.
How is this different from a scalar field - a scalar function of space?
The exterior derivative of the 0-form f is f_{x}dx+f_{y}dy+f_{z}dz
(f_{x} denotes the partial of f with respect to x.
How is this different from GRAD f (dot ) dr ?
What is this new language adding to good old fashioned vector analysis?