Formulas of Vectorial Analysis

`(f g) = ` f `g

` · (To B) = ` · To ` · B

` ^ (To B) = ` ^ To ` ^ B

` · (fTo) = ` f · To f (` · To)

` ^ (fTo) = ` f ^ To f (` ^ To)

` · (To ^ B) = B · (` ^ A) - To · (` ^ B)

` ^ (To ^ B) = (B · `)A - B(` · To) - (To · `)B To(` · B)

`(To · B) = (B · `)A (To · `)B B^(` ^ To) A^(` ^ B)

` ^ (` f) = 0 the rotor of the gradient of a function to climb is null

` · (` ^ To) = 0 the divergence of the rotor of a vectorial function is null

` ^ (` ^ To) = ` (` · To) - ` ²To

 

Length of one curva :

 

 

Abscissa curvilinea :

 

 

Curvilinear integral of 1ª species :

 

 

Coordinated barycentre of a thread :

 

 

Moment of inertia of a thread :

 

 

Volume of a solid one of spin (Pappo) :

 

Curvilinear integral of 2ª species :

Calculation of upgrades them :

 

Normal payer to one surface :

 

Slowly tangent to one surface in a point : = 0

 

 

Area of one surface :

 

 

 

Formula of Guldino :

 

Integral of surface of one function h :

 

Theorem of Green in the flat :

 

 

Calculation areas by means of Green Gauss:

 

Theorem of Stokes :

 

 

Theorem of the divergence of Gauss :