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16 intégrales curvilignes, formes différentielles
- 1. =
!
"#
$% →γ
! →
& γ
γ
"#
= "#""##"#
γ
# ' "#"# = "
! ( ) * # ) + ,
" +
-
. .
/ 010 + γ . ) =<<<=
$% + [ ] $2% −
∈∀ γ
#& 3 "
) ( *
=
−
+∞→
−= ""#"#""###"#
γ
# "
' [ ]4∈ −
+= # ) 5 $% "
6
7. ) γ +
"# # "
γ
"#
! Ω
" 8
6 Ω Ω "#
! . = + "# # " 0
) 9 "#
"# "# + ,
touscours.net
- 2. ω Ω ,
++=ω ' Ω
"#"#"#"#"# ++=∈∀ ω
& + ω +
8 : = Ω ,
+=ω ' Ω
7.
0 ω ++=∈∀ "#"#"# ω
0 ! →
∂
∂
+
∂
∂
=
Ω
;" < .
8
! ω Ω & + ω . + ,
. Ω + =ω
= .
= ω "#"#"#"# +=Ω∈∀ ω
# ' " . . +
Ω∈∀ "# "#"#
∂
∂
= "#"#
∂
∂
=
" , , )
!
"#
$% →γ
& )
& = ""#""###ωω
γ
""##Ω∈ω "#""## ∈ω ∈""#""###ω
=
! "#"#"#"# +=Ω∈∀ ω
[ ]+= "#/""#"##"#/""#"##
γ
ω
! ( ) * +
, # ,
, "
touscours.net
- 3. =
===
γγ
ωωωω ""#"##"#""#""###""#"#""###
& . .
'ω .
> 5
! →Ω →$%γ
. Ω
"#"# −=
γ
' γ 5
5
7 γ # / 010 = " 4=
γ
8
= .
[ ] "#"#""#"##"#/""#"##"#/""#"##
""#"##
−==
∂
∂
+
∂
∂
=
γ
ω
! Ω →Ω 4
& ""#"#"##"#"# =Ω∈∀
! ω ++=ω
γ
ω ⋅
γ
"# γ
?
[ ]
=
−
+∞→
⋅=
⋅=
++=
""##
"#"#
"#/""##"#/""##"#/""##
γ
ω
&' −
+= "#=
#= 5 "
5 ,
"#"# −=⋅
γ
# , , "
' →Ω
touscours.net