~ ?yvD ?Dy
???

¥ w
s
~ ?yvD ?Dy
Baà
Q¥? ?
? w
Σ
^;á¥,
¥
á1 ?
?f
),,( zyxρ, p
¥é
,
L è
asé
:l v ?is?| n∑
n
SSS,,,
21
L
aí

,),,(
iiii
S?∈? ζηξ
niS
iiii
,,2,1,),,(L=?ζηξρ
a p

=
n
i
iiii
S
1
),,( ζηξρ
a |K

=

n
i
iiii
S
1
0
),,(lim ζηξρ
λ
~ ?yvD ?Dy
=a
¥ w
s¥?l

! w
Σ
^;á¥
f
),,( zyxf  Σ
μ?
ü Σs? nl v
i
S? 
i
S? ]
H9V
U
? il v w
¥

!? ),,(
iii
ζηξ 1
i
S?

?i |?¥?
Te?),,(
iii
f ζηξ
i
S? 

iT

=
n
i
iii
f
1
),,( ζηξ
i
S?
 ?T?òl v w
¥°?¥Kv′ 0→λ
H
?
T¥Ki
5?NK1f
),,( zyxf  w
Σ


¥ w
s ?B ? w
s 
?l
~ ?yvD ?Dy
?N?l
,
^B;á w
! ∑
asé,l v ?is?| n∑
n
SSS,,,
21
L
aTe
,),,(
iiii
S?ζηξ ∈? niSf
iiii
,,2,1,),,(L=?ζηξ
a p

=
n
i
iiii
Sf
1
),,(?ζηξ
a |K

=

n
i
iiii
Sf
1
0
),,(lim?ζηξ
λ
?T

Ki
5??K′1f
,

¥ w
s w
∑,),,(:
∫∫

dSzyxf:1
,),,(
¥μ?f
^?l ∑zyxf
),,( zyxf
~ ?yvD ?Dy
'
∫∫
Σ
dSzyxf ),,(
iii
n
i
i
Sf?=

=

),,(lim
1
0
ζηξ
λ
∫∫
Σ
=dSzyxf ),,(
∫∫∫∫
ΣΣ
+
21
),,(),,( dSzyxfdSzyxf,

¥ w
s¥?é
5# Vs1s
;ᥠw
?,
21
ΣΣΣ
?$f
 ? ),,( zyxf,?s w
Σ
~ ?yvD ?Dy
p/
 w
s¥′
,4,.1
222
=++∑ zyx
=
∫∫

ds45
-W¥?sDo? w
01,.3
22
==+=∑ zzyxz
=?+
∫∫

dszyx )(
22
5
,4,.2
222
=++∑ zyx
=++
∫∫

dszyx )(
222
5
π64
π64
0
~ ?yvD ?Dy
?a9
E;1)],(,,[
22
dxdyzzyxzyxf
xy
D
yx
∫∫

+

+=
∫∫
Σ
dSzyxf ),,(
),(:.1 yxzz =Σ ? w
5
?v w
¥?] f ?s1[/ ??
~ ?yvD ?Dy;1]),,(,[
22
dxdzyyzzxyxf
xz
D
zx
∫∫

+

+=
∫∫
Σ
dSzyxf ),,(5
.1],),,([
22
dydzxxzyzyxf
yz
D
zy
∫∫

+

+=
∫∫
Σ
dSzyxf ),,(
),(.3 zyxx =Σ ? w
5
),(:.2 zxyy =Σ ? w
~ ?yvD ?Dy
∫∫
Σ
dSzyxf ),,(
¥9
E??
??g?Z_.1
pg? u×¥A
TZ? w
,.2 ∑
¥Vr
T p dS.3
1=×s.4
~ ?yvD ?Dy
9
∫∫
++
Σ
dSzyx )(, ? Σ1
ü
5=+ zy $?
25
22
=+ yx
?¤¥?s,
è
s w
Σ yz?= 5,
3
g?× 
}25|),{(
22
≤+= yxyxD
xy
~ ?yvD ?Dy
∫∫
++
Σ
dSzyx )(#
∫∫
++=
xy
D
dxdyyyx )5(2
∫∫
+=
xy
D
dxdyx)5(2
rdrrd
∫∫
θ+θ=
π 5
0
2
0
)cos5(2
.2125 π=
dxdyzzdS
yx
22
1

+

+=
dxdy
2
)1(01?++=
,2dxdy=
~ ?yvD ?Dy
è 9
dSxyz
∫∫
Σ
||,
? Σ 1
t
22
yxz += 
10 ≤≤ z ,
3 G???
$f
|| xyz1?
xayaz
^
}f
à?1?
t
z
yxz
22
+=

∫∫∫∫
ΣΣ
=
1
4 ? ? 
(
1
Σ 1?B?K?s w
)
x
y
z
~ ?yvD ?Dy
dxdyzzdS
yx
22
1

+

+=
dxdyyx
22
)2()2(1 ++=
e
T dSxyz
∫∫
Σ
= ||
dSxyz
∫∫
Σ
=
1
4
dxdyyxyxxy
xy
D
2222
)2()2(1)(4 +++=
∫∫

? 1|),{(
22
≤+=

yxyxD
xy
,}0,0 ≥≥ yx
~ ?yvD ?Dy
?¨US trx cos=,try sin=,
rdrrrttrdt
∫∫
+?=
1
0
222
2
0
41sincos4
π
drrrtdt
2
1
0
5
0
412sin2
2
+=
∫∫
π
7
2
41 ru +=
du
u
u
2
5
1
)
4
1
(
4
1?
=

.
420
15125?
=
~ ?yvD ?Dy
è
3
4321
∑+∑+∑+∑=∑
,0:
1
=∑ x,0:
2
=∑ y,0:
3
=∑ z
,1:
4
=++∑ zyx
,1 yxz=
xyxD
xy
≤≤≤≤ 10,10:
dxdydxdyzzdS
yx
3)()(1
22
=

+

+=
∫∫

xyzdS
∫∫=
xy
D
dxdyyxxy 3)1(
∫∫
=
x
dyyxxydx
1
0
1
0
)1(3,
120
3
=
,
∫∫

xyzdS9
w
s
1,0,0,0,=++===∑ zyxzyx #
.
? ?8¥V
1
Σ
x
o
z
y2
Σ
3
Σ
4
Σ
~ ?yvD ?Dy
9
∫∫
Σ
xdS, ? Σ
^??
1
22
=+ yx,
ü
2+= xz # 0=z
??¥ bW ?8¥V
,
è
~ ?yvD ?Dy
3
∫∫∫∫∫∫∫∫
ΣΣΣΣ
++=
321
?
1
Σ  0=z,
2
Σ  2+= xz,
3
Σ  1
22
=+ yx,g?×
1
D  1
22
≤+ yx
A ? 0
11
==
∫∫∫∫
Σ D
xdxdyxdS,
,011
12
=+=
∫∫∫∫
Σ D
dxdyxxdS
~ ?yvD ?Dy
)
3
Σ
H,|g?×ê xoz
,

?i
2
1 xy?±= s1Pa·


∫∫
Σ
3
xdS
∫∫
Σ
=
31
xdS
∫∫
Σ
+
32
xdS

P·

g?M]
∫∫

+

+=
xz
D
zx
dxdzyyx
22
12
xoz
~ ?yvD ?Dy
∫∫
+=
xz
D
dxdz
x
x
x
2
2
1
12
∫∫
+
=
1
1
2
0
2
1
2
x
dzdx
x
x
,π=
∫∫
Σ
∴ xdS π=π++= 00
.
~ ?yvD ?Dy
9
dSzyx )(
222
++
∫∫
Σ
, ? Σ1
=¤? o
2222
azyx =++ ¥?
8 azyx =++ |||||| V
,
è
$f
=),,( zyxf
222
zyx ++,3
1?US
ae? (?,
s w
Σ9 μ??,
#es
∫∫∫∫
ΣΣ
=
1
8,
( ?
1
Σ V
U?B?K?s w
)
~ ?yvD ?Dy
1
Σ  azyx =++,' yxaz=
dxdyzzdS
yx
22
1 ++=
dxdy3=
dSzyx )(
222
++
∫∫
Σ
∫∫
Σ
++=
1
)(8
222
dSzyx
dxdyyxayx
xy
D
∫∫
++= 3])([8
222
.32
4
a=
~ ?yvD ?Dy
1al2
2
¥ w
s¥9
^| 1g?×

¥=×s9
,
?v w
¥?] f ?g?? ?
US

1
¥ w
s¥à
Q ;
∫∫
Σ
dSzyxf ),,(
iii
n
i
i
Sf?=

=

),,(lim
1
0
ζηξ
λ
?iBga=}a ?D
~ ?yvD ?Dy
± I5

¥ w
s1=×s
¥
T?,μy0,
k
a
ü
??y0¥+il,
22
1
yx
zz ++
~ ?yvD ?Dy
± I53s
^ w
í¥
,
dS
22
1
1
),cos(
yx
zz
zn
++
=
22
1
yx
zz ++
#
^ w
ELD àC?¥??
¥?
,
z
~ ?yvD ?Dy
°z A b5
a X? w
∑¥
a1
5 =
∫∫

ds10 @@@@@@@ 
a
∫∫

dszyxf ),,( 
∫∫
yz
D
zyzyxf ),),,(( @@@@@@@@dydz 
a
! ∑1 o
2222
azyx =++  xoy
ü
¥
Z?s
5 =++
∫∫

dszyx )(
222
@@@@@@@@@@@@ 
a =
∫∫

zds3 @@@@@
? ∑1
t
)(2
22
yxz +?= 
xoy
Z¥?s 
a =+
∫∫

dsyx )(
22
@@@@@@
? ∑1
22
yxz += #
ü
1=z
??¥ u×¥??H? w

5
~ ?yvD ?Dy
=a9
/

¥ w
s
a
∫∫

+ dszxxxy )22(
2

? ∑1
ü

 622 =++ zyx ?B?K?¥?s 
a
∫∫

++ dszxyzxy )(
? ∑1
22
yxz += $
?
axyx 2
22
=+
?¤¥μK?s
?a p
t
T )10)((
2
1
22
≤≤+= zyxz ¥é

N T
¥
á¥vl1 z=ρ 
1a p
t
T )10()(
2
1
22
≤≤+= zyxz ¥é
N
 T¥
á¥vl1,z=ρ 
~ ?yvD ?Dy
5s?
Baa a10  a
22
)()(1
z
x
y
x
+
+ 
a
4
2 aπ  a π
10
111

a π
2
21+

=aa
4
27
 a
4
2
15
64
a 
?a
6
π

1a )136(
15
2
+
π