Intuitive, but correct, explanation of differential calc. of several variables


 Click on this link for the paper:


(Warning!  It assumes you know about lines, planes, vectors, cross products, etc…but that is about all.)

From the abstract:

“..describes an approach I use when I teach difierential calculus ofseveral variables. It has the benefit of giving the students a single image from which they can visualize any of the tools described in the title(the gradient, the differential, the tangent plane, the directional derivative, the chain rule, and partial derivatives) and see how to go from that visualization to the necessary computations. Thus, they learn not only the geometric concepts in calculus of several variables, but, they also lea,rn how to translate geometric ideas into mathematical computations. I have had considerable succes.s with this method with students of varying abilities…”