Post on 14-Mar-2016
description
. = .
. y = f (x) [a, b]. i[xi, xi+1], xi = xi+1 xi , [xi, xi+1], f ( i) xi.
. xy D, z , z= f (x, y)0, . . xy . = . 1.V.
(i)D n D1, D2,, Dn , Di .z = f (x,y)z = f (x,y)DiDi
(ii)Di, z = f (x,y), . ( i , i) Di . = f ( i , i). i = Di. = f ( i , i) i
(iii), , V, "", V.
(iv) DiDi. ( i , i) Di , i = Di .
1. 2. 3. 4.
Dn
i
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EMBED Equation.3 .
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D
Dn
i
EMBED Equation.3
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D
EMBED Equation.3 .
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------
(1) .
(3)
.
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(2)
D
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D
k
D
D
D
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6
1
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.
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,
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D
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.
: ;
XX y .
X--- y x
Y--- x y
1. D x, y. , , .
2.1
2 f (x, y) = f1(x)f2(y),
Da x b, c y d. f (x, y) = f1(x)f2(y)
.3.
4.D: y1(x) y y2(x), a x b, x .y2(x). y2(x), . DD1, D2, .
1 D D Y
2
D D X
3
,
:
.
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().
(
),
,
[0,1]
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6
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7
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().
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=
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8
D
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9. .D.D y x 1, 0 y 1 x=y x=1y=0, y=1. =
89
1.
2. x .
2.
, y , ?
3.
1
1D 2D
2D 3D
3D 4D
4D
2
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3
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D
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4. Dx2+y2 1, Dx2+y2x=rcos, y=rsin, x2+y2 1r = 1.(2)D*: 0 r 1, 0 2
5
D
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6
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(),
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,
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EMBED Equation.3 .
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7
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(),
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EMBED Equation.3
=
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5
D
1 xoy V1 V = 4V1
2
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x
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DA
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.
S: 0 y R, 0 x R