Is the "gradient" vector a concept that that is coordinate independent ? For example, the concept of a vector representing a force is independent of what coordinate system is used to represent the vector. So is a "gradient vector" such a physical vector ? The web page http://www.mathpages.com/home/kmath398/kmath398.htm says that the temperature at a point in space is invariant under coordinate transformations, but the gradient of the temperature at a point in space is not. I can understand that view if "gradient" always implies a choice of coordinate system. Does it ? - or should we protest to the authors of that page ?