Derivatives and Integrals
We have differentiated vector components on page 25 and have introduced the comma notation for the derivatives in definition (2.12). In rectilinear coordinates the changes of the vector components indicate the change of the vector. This is no longer so when the coordinates are curvilinear. As a simple example consider Figure 5.1 a. It shows a polar coordinate system and in it three vectors v. The vectors are equal, but their radial components v1 are not and neither are the circumferential components v2. On the other hand, the vectors in Figure 5.1b are different, but they have the same radial component v1 and the same circumferential component v2 = 0.
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