In previous videos we established differentials as elements of the epsilon neighborhood of zero. Further, we found a multiplicative semi-group algebra on the dx's, and finally established a closed additive algebra of differentials that is homomorphic to addition on the real numbers. These results open up a flood of new applications for differentials. Here we develop Linear Spaces of differentials that are companions to corresponding Linear Spaces over the reals. They are linear spaces of vector differentials. BTW be sure to turn on annotations, they contain good stuff and necessary corrections.
