المحاضرة التاسعة عشر

59
( Analytic Functions )
z0 w = f (z) ?
z0 z0
D w = f (z) ?
D
( Entire function ) w = f (z) ?
z0 z0 z0 f ?
f (z) ( singular point )
z0 ? (Isolated point) z0 ?
z0 z0
?
z = ± i z= 0
w = f (z) =
z = 1 z
z = 1
1 + z
1 - z
dw59
( Analytic Functions )
z0 w = f (z) ?
z0 z0
D w = f (z) ?
D
( Entire function ) w = f (z) ?
z0 z0 z0 f ?
f (z) ( singular point )
z0 ? (Isolated point) z0 ?
z0 z0
?
z = ± i z= 0
w = f (z) =
z = 1 z
z = 1
1 + z
1 - z
dw
dz
2
(1 – z)2
( 1)
( ) 1 2 2 ?
?
?
z z
f z z
60
2
( Polynomial )
3
z = 0 f (z) = 2
z = 0
z
dz
2
(1 – z)2
( 1)
( ) 1 2 2 ?
?
?
z z
f z z
60
2
( Polynomial )
3
z = 0 f (z) = 2
z = 0
z59
( Analytic Functions )
z0 w = f (z) ?
z0 z0
D w = f (z) ?
D
( Entire function ) w = f (z) ?
z0 z0 z0 f ?
f (z) ( singular point )
z0 ? (Isolated point) z0 ?
z0 z0
?
z = ± i z= 0
w = f (z) =
z = 1 z
z = 1
1 + z
1 - z
dw
dz
2
(1 – z)2
( 1)
( ) 1 2 2 ?
?
?
z z
f z z
60
2
( Polynomial )
3
z = 0 f (z) = 2
z = 0
z