%%HP: T(1);
"IFORMULAIRE D'Analyse vectorielle

IGradient
        
  �    ˆf/ˆx
grad f ˆf/ˆy
       ˆf/ˆz
     �       �
df= grad f. dM
    �
„„f.dS=„„„(grad f dV)

IDivergence
    �
div A = ˆAx/ˆx+ˆAy/ˆy+ˆAz/ˆz
  �  �          �
„„A .dS=„„„(div A dV)
(Green Ostr)

IRotationnel
  �    ˆAz/ˆy - ˆAy/ˆz
rot A  ˆAx/ˆz - ˆAz/ˆx
       ˆAy/ˆx - ˆAx/ˆy
  � �       �   �
„(A.dl)=„„(rotA.dS)
(Stokes)
    �            � �
„„„(rotA dV)=-„„(A^dS)

ILaplacien scalaire
Lf=ˆ²f/ˆ²x+ˆ²f/ˆ²y+ˆ²f/ˆ²z
Lf=div(gradf)

ILaplacien vectoriel
�   LAx
LA  LAy
    LAz
�   �       �   �   �  �
LA=grad(div A)-rot(rot A)

IRelations usuelles
rot(grad f)=0
div(rot A)=0
A^(B^C)=(A.C)B-(A.B)C
grad(fg)=f gradg+g gradf
div(fA)=f divA+A.gradf
rot(fA)=f rotA+gradf ^A
div(A^B)=B.rotA-A rotB
rot(A^B)=A divB-BdivA+(B.grad)A-(A.grad)B
(A.grad)A=0.5grad(A^2)-A^rotA
rot(rotA)=grad(divA)-LA


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