differential coefficients of the second order of
with respect to
and
[1]
161. The operators
and
may be applied to dyadics in a manner entirely analogous to their use with scalars. Thus we may define
and
by the equations
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Then, if
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Or, if
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162. We may now regard
in expressions like
as representing two successive operations, the result of which will be
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in accordance with the definition of No. 70. We may also write
for
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although in this case we cannot regard
as representing two successive operations until we have defined
[2]
That
will be evident if we suppose
to be expressed in the form
(See No. 71.)
163. We have already seen that
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where
and
denote the values of
at the beginning and the end of the line to which the integral relates. The same relation will hold for a vector; i.e.,
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- ↑ We might proceed to higher steps in differentiation by means of the triadics
the tetradios
etc. See note on page 74. In like manner a dyadic function of position in space (
) might be differentiated by means of the triadic
the tetradic
etc.
- ↑ See footnote to No. 160.