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Unformatted text preview: potential. 2.5. TENSOR FIELDS OF HIGHER RANK A system such as the threedimensional Euclidean metric tensor gij has nine components when i and j range over 1, 2, 3. Such quantities are given special names when their components in any two coordinate systems are related by specific transformation laws. Covariant tensor field of rank two, t i j Contravariant tensor field of rank two, tij 'The variables Bi and 8", in general, are not so related [see Eq. (2.3:9)]. Thus, although the differential doi is a contravariant vector, the set of variables Bi itself does not trans form like a vector. Hence, in this instance, the position of the index of Bi must be regarded as without significance....
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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.
 Fall '05
 Thomson

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