Download - 21.5 三重积分
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EMBED Equation.3
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EMBED Equation.3
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T : x = x(u, v, w), y = y(u, v, w), z = z(u, v, w) uvw uvw xyz xyz , 1) x=x(u, v, w), y= y(u, v, w), z=z(u, v, w)C1(uvw)
5. .:
2) 0, (u, v, w)uvw f (u, v, w)R(),
(5),
M (x, y, z) (r, , z)()x = r cos y = r sin z = z
z r =, z =, z z =, z .
= r
,, r z :r1( ) r2( ),z1(r, ) z2 (r , )). ,
6.: , xy D :, z = z.
*
7.: xy D : x2 + y2, , z = z.
*
9. x2+y2=2x,, xy , V: , x = rcos y = rsin z = z z = r: r = 2cos
, V1, V=2V1. xy D:D={(x, y)|x2+y22x}.,1()1*:
11. : ,
, D D* :
M (x, y, z) (r, , ) ()
x = r sin cos y = r sin sin z = r cos r = , o = , z = , , z .
r , , . x2 + y2 + z2 = r2
8. , .: . r = a, ,
(.)
9. z = 0.:
10. V.: yzxzxy1V1
. : (1)
xoy + z
zr z r
6 (1) (2) zr xoy (r, )D z
(r, )D z
xoy
6
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(r, )D z
7 xoy (r, )D z
(r, )D z
r r
8 r (1) xoy
9 xoy
10
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P251: 123, 4, 5.
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9.3
f(x y z) nv1 v2 vn vii vi(i i i)
f(x y z) f(x y z)dv dv x y z
vixi yizi dvdxdydz
1 {(x y z)| z1(x y)zz2(x y) y1(x)yy2(x) axb} >>> >>>
{(x y z)|(x y)Dz c1zc2} Dzz
2 M(x y z) MxOyP P( ) zM z 0