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Sec. 2.8
RECTANGULAR CARTESIAN TENSORS
43
any set of functions of the requisite number.
A
tensor field thus assigned
in a given frame of reference then transforms according to the tensor trans
formation law when admissible transformations are considered. In other
words, once the values of the components of a tensor are assigned in one
particular coordinate system, the values of the components in any general
coordinate system are fixed.
Why are the tensor transformation laws in harmony with physics? Be
cause tensor analysis is designed so. For example, a tensor of rank one is
defined in accordance with the physical idea of a vector. The only point
new to the student is perhaps the distinction between contravariance and
covariance. In elementary physics, natural laws are studied usually only
in rectangular Cartesian coordinates of reference, in which the distinction
between the contravariance and covariance disappears. When curvilinear
coordinates are used in elementary physics, the vectorial components must
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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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