1 In this chapter, as in the previous one, we keep our discussion limited to the ordinary three-dimensional space. This space has special significance because the usual physical processes can be best described in it.
2 It is possible to define a gradient for a vector function as well, using its components. However, its notation and interpretation becomes a little tricky and its relevance is appreciated only in certain special applications.
3 Continuous tangency over a straight segment poses no difficulty.
4 Any lateral (vertical) face has a zero projected area and hence makes no contribution.
5 Note that this has little connection with ‘Green’s theorem in the plane’ discussed earlier, which is rather more in continuity with Gauss’s ...