00070___436023d2cfea430c0cd3ff0e3094b804 - Sec. 2 .13 T...

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Sec. 2.13 TENSOR EQUATIONS 49 which can be reduced to (4) But this states that the functions d[A/dxp + r'2p[s are the components of a mixed tensor of rank two. Hence, the functions are the components of a mixed tensor field of rank two, called the covariant derivative the contravariant vector 9. We shall use the notation tila for the covariant derivative of t'. By a slight variation in the derivation, it can be shown that the are the components of a covariant tensor field rank two whenever .$ are the components a covariant vector field. This is called the covariant &, and is denoted by <ita. More generally, a long but quite straightforward calculation analogous to the above can be made to establish the covariant derivative a tensor Till.::bp,p of rank p + q, contravariant of rank p, covariant of rank
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This note was uploaded on 01/04/2012 for the course ENG 501 taught by Professor Thomson during the Fall '05 term at MIT.

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