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Stokes'theorem
Exercise4.2
1.
Prove the following equation holds for any surface
and its boundary
in the common domain of the scalar fields
..
2.
Let
and
be a scalar field. Then prove the following equation holds for any surface
and its boundary
.
(1)
(2)
(3)
3.
Prove the following holds for any surface
and its boundary
in the common domain of the scalar field
and the vector field
.
4.
Let
and
be a scalar field. Prove that for any surface
and its boundary
, the following equation holds.
5.
It is assumed that the vector field
is defined in the whole space..About the border
of any curved surface if
has a scalar potential. Prove this.
6.
For
,show that Stokes' theorem holds.
7.
Find
.where
is a curve connecting from the point
to
and back to the starting point..
8.
For any surface
and its boundary
within the common domain of
, prove the following equation holds.
9.
Let
.Prove for any surface
and its boundary
, the following is true.
(1)
(2)
Next:
Exercise Answer
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Integral formula
Previous:
Gauss's divergence theorem
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