Chapitre 16 :Intégrales curvilignes, formes différentielles
Transcription
Chapitre 16 :Intégrales curvilignes, formes différentielles
T his work is licensed under a Creative Commons “Attribution-ShareAlike 4.0 International” license. = γ % ! $→ #" → ! γ & γ # = " # ! # "= # ' # "" # " ( # γ " #" " ) *# + " ) +, . 010 / % + ∀ ∈[ + $ γ . ]γ . 2% < < < = $ − #& 3" ) γ # ( = " ∈ [4 ' 6 7. → +∞ ] # ""# # " − # # = = + − − * "" # " # ) 5 $" % γ ) "# # ! = ) " γ # + " Ω "8 6 ! # " Ω = ) . # " Ω + # # " " # 9 " # +, Ismaël Bouya http://melusine.eu.org/syracuse/immae/ 0 " ω= + ω + Ω , Ω ' ∀# "∈ ω# & + ω 8 : = ' ω= + "= # " + # + , Ω ∀# "∈ ω# "=# + " → = Ω ;" < ∂ ∂ + + ∂ ∂ . 8 ! ω Ω & + ω= . Ω . = ω = # ' ∀# " Ω 7. 0 ω 0 ! + # " "∈Ω " ∂ "= # ∂ # " ∀# . " # "= ∂ # ∂ + " ∈ Ω ω# . γ % $→ , ω= γ ) ω # # ""# # "" ω ∈ #Ω # " ∈ Ω ω# ! ∀# ! + # ) & ω= " +, #" & γ "= # . " , ! ω [ "" ω # # "" ∈ # = "= # " + # " " ω # # ""# # "" ∈ # # " # "" / # " + # # " # "" / # "] ( ) * + , #, , " " + = ω= ω # # ""# # " # "" γ ω # # ""# # "" # " = & = ω# γ "# # . 'ω . 5 Ω→ > ! = # "− # " γ 5 7 . γ % Ω ' . γ # / $→ γ = 010 8 " γ = 5 =4 . ∂ ∂ # # " # "" / # " + # # " # "" / # " ∂ ∂ ω= γ "" = [ # # " # ""] = # " − # " # # " # "" ! & ! Ω ω ∀# "∈Ω Ω→ "=# # " # ω= + + # ω γ " # "" γ "⋅ # γ 4 ? ω= γ = = [ # # "" / # " + # # # "" ⋅ = &' = + #= 5 = − − # " " 5 γ ' ⋅ Ω→ # "" / # "] "⋅ # " # → +∞ # "" / # " + # = # "− # " # , , , "
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