# 当   R 3 ， 有 X =( x , y , z )  , d  = d v

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. . z. . d z. d x. d y. y. x. 0. 9-3. . R 3 X =( x , y , z ) , d = d v. . . 1. . . d v =d x d y d z. . z. z = z 2 ( x , y ). y. z = z 1 ( x , y ). D. x. 0. (1) . y = y 2 ( x ). a. b. - PowerPoint PPT Presentation

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• R3 X=(x, y, z) , d = dv1. dv=dxdydz9-3.

• (1) D xy .y=y1(x)bay=y2(x)

• 1. x+y+z=1. D: 0 y 1x, 0 x 1

• 2. y=0, z=0,

• y=y1(x, z)z0y=y2(x, z)Dxzyx

• x=x2(y, z)z0x=x1(y, z)Dyzyx

• 3. z= x2+y2 z=1. z xy .z= x2+y2 x2+y2=1 D: x2+y21z=1z=1

• xyz01Dxyz=1z= x2+y2

• 2 y xz z= x2+y2 Dxy: x2 z 1,z=1 1 x1z= x2+y2 x

• (2) :(x, y)D(z), z1zz2

• 4. z=x2+y2 z=1.D(z): x2+y2zz[0, 1]

• 5. D(x): 0 y 1x, 0 z 1xyx : 0 x 1 x+y+z=1.

• 2. T uvw * xyz (1) x=x(u, v, w), y=y(u, v, w), z=z(u, v, w)C1(*)

• (2) (u, v, w)* 0

• (3) T : * f (x, y, z)C( )

• 3. M (r, , z)x=rcosy=rsinz=z(0r
• r==z=

• = r dxdydz=rdrddz

• 1. z=1 . D: x2+y21 z =rz=rz=1

• D

• 2. ={(x, y, z) | x2+y2+z21, z0}. D: x2+y21

• 3. 1 z=1 . = D() 0 2 =

• xzy

• 4. 2 ={(x, y, z) | x2+y2+z21, z0}. = D() 0 2 =

• xyz0

• 4. M (r, ,)x=OPcos z= r cos(0r
• r = = =dxdydz= r2sin drdd

• 5. ={(x, y, z) | x2+y2+z21, z0}. x2+y2+z2=1 r=1 0 2 = D()

• xyz0z

• 6. x2+y2+z2=a2 . x2+y2+z2=a2 r=a

• 7. x2+y2+(z1)21. x2+y2+(z1)21 r=2cos1. x2+(y -1) 2+z21 2.