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Multiple integrals.
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Applications of the derivative.
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The curl of a
The divergence of a vector field in the space.
Definition 6.37
Let
be a vector filed in the 3-dimensional space. The
divergence
of the vector field
is the scalar function
It has the same physical interpretation as the divergence of a vector field in the plane (v.s. Remark
6.34
).
Remark 6.38
The divergence of the vector field
can be expressed as the formal scalar product
where
Remark 6.39
Let
f
(
x
,
y
,
z
) be a function of three real variables defined on an open domain
in
. Then ,as we saw in
6.18
, the gradient of
f
is:
Apply the divergence operator to this vector field (=the gradient field); we have:
i.e.
is Laplace's operator.
More on this topic will be studied in Section
5
, about the Divergence Theorem.
Next:
Multiple integrals.
Up:
Applications of the derivative.
Previous:
The curl of a
Noah Dana-Picard
2001-05-30