第 3 章 复变函数的积分
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Transcript of 第 3 章 复变函数的积分
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3
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: 3.1: 3.2: -()3.3: 3.4: 3.5: 3.6: 3.7:
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:
(1) (); (4)
(2) (,);
(3) ;
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3.1 3.1.1
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3.1.1 (1) . .
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(2)
(3)
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3.1.2 3.1 n ,
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n L L
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x
y
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EMBED Equation.DSMT4
EMBED Equation.DSMT4
EMBED Equation.DSMT4
EMBED Equation.DSMT4
3.1
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3.1.3
LL . ,
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L (3.1.3)
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(1) L (2) .
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3.1.3
3
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(1)
3.1.6 (2) 3.1.7 (3)
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(4) 3.1.9 (5)
(3.1.10)
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6 (3.1.11)
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3.1.4 3.1.2C 3.1.1 C3+4i
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3.1.2
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3.1.3
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L
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3.1.5
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,
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3.2
3.2.1
3.1.1
3.1.2
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1825 3.2.1 L L 3.2.1 3.2.2
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3.2
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C-R
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, . (Cauchy)1825(Goursat)1900.
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[1]DL [2]
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[3]Green
L [4]
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3.2.2
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3.3,
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3.2.2 3.2.3 3.2.2
3.2.4
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3.2.4 D
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3.2.7
3.2.53.2.63.2.7,
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3.2.1
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3.2.5 3.2.6 ,
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3.2.5,
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3.2.3
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3.2.1
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3.2.2 1
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3.2.3 1
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2 3.1.3 (3.1.12)
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3.2.4
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3.2.4
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3.3
3.3.1
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EMBED Equation.DSMT4
EMBED Equation.DSMT4
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n1.
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1 3.3.32 (3.3.4) 3.3.2 L 3.5 L L DD
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(i) (ii) (iii)
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b
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3.6
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1 . 3.6
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3.3.1
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3.3.2
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2
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3.4 3.4.1 3.4.1 DLDD, L (3.4.1)
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R R
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3.8
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3.4.1
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1
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1 C
2
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3.4.2
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3.4.2
3.4.2 LD
L
D
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(3.4.3)
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L
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3.9
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3.4.3 1;(2).
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1 3.4.3 L L (3.4.4)
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3.10
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L L 3.10 (3.4.5)
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R
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(3.4.5)
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1 2
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3 3.10
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3.4.3
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2. 3.4.4 LL
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3.4.3
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3.5 3.5.1
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3.5.1 n (3.5.1)
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EMBED Equation.DSMT4
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3.11. . C. . D D.
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3.5.2 3.5.2 C 3.5.2
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(3.5.2)
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3.5.33.5.3 C:
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3.5.4.
3.5.4 (Liouwille)
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n=1
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3.5.5 3.5.5Morera , (3.5.5)
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3.2.3 3.2.4
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3.5.6 n
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P88 3.3; 3.5;3.7: 3);(4);3.8: (2); (5); (6);3.10; 3.12; 3.14;3.15; 3.16
3.19