16 intégrales curvilignes, formes différentielles
3
= ! " # $ % → 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
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Transcript of 16 intégrales curvilignes, formes différentielles
=
!"#
$%
→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
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∈∀ "# "#"#
∂∂= "#"#
∂∂=
" ,,)
!"#
$%
→γ
&)
& =
""#""###
ωωγ
""## Ω∈ ω "#""##
∈ω ∈""#""### ω
=
! "#"#"#"# +=Ω∈∀ ω
[ ] +=
"#/"" #"##"#/"" #"##
γω
! ()* +
,#,
,"
touscours.net
=
===γγωωωω
""#"##"#""#""###""#"#""###
&. .
'ω .>5
! →Ω →$%γ
. Ω
"#"# −=γ ' γ 5
5
7γ #/010 = " 4=γ
8
= .
[ ] "#"#""#"##"#/"" #"##"#/"" #"##
""#"##
−==
∂∂+
∂∂=
γω
! Ω →Ω
4
& ""#"#"##"#"# =Ω∈∀
!ω ++=ω
γω ⋅γ
"#
γ
?
[ ]
=−+∞→
⋅=
⋅=
++=
""##
" #"#
"#/"" ##"#/"" ##"#/"" ##
γω
&'
−+= "# =
#=5"
5,
"#"#
−=⋅γ #,,"
' →Ω
touscours.net
