The Geometric Definition of the Gradient

We are accustom to the standard definition of the gradient vector field as (f_x, f_y, f_z); however, this definition is not coordinate invariant. We give the coordinate invariant definition of the gradient geometrically in three dimensional space before giving the tensorial definition. This will give us a flavor of the more general result. #mikethemathematician, #profdabkowski, #mikedabkowski