ecuacions de camps

∯ [ E(x,y,z) ] d[(yz,zx,xy)] = Q(x,y,z)
∯ [ B(x,y,z) ] d[(yz,zx,xy)] = A(x,y,z)

∯ [ E(x,y,z) ] d[(yz,zx,xy)] = ∭ [ div[ E(x,y,z) ] ] d[x]d[y]d[z]
∯ [ B(x,y,z) ] d[(yz,zx,xy)] = ∭ [ div[ B(x,y,z) ] ] d[x]d[y]d[z]

div[ E(x,y,z) ] = d_{xyz}^{3}[ Q(x,y,z) ]
div[ B(x,y,z) ] = d_{xyz}^{3}[ A(x,y,z) ]

d_{t}[ E(x,y,z) ] + rot[ E(x,y,z) ] = J(x,y,z)
d_{t}[ B(x,y,z) ] + rot[ B(x,y,z) ] = H(x,y,z)

∯ [ d_{t}[ E(x,y,z) ] ] d[(yz,zx,xy)] = ∯ [ J(x,y,z) ] d[(yz,zx,xy)]
∯ [ d_{t}[ B(x,y,z) ] ] d[(yz,zx,xy)] = ∯ [ H(x,y,z) ] d[(yz,zx,xy)]

div[ d_{t}[ E(x,y,z) ] ] = div[ J(x,y,z) ]
div[ d_{t}[ B(x,y,z) ] ] = div[ H(x,y,z) ]

rot[ E(x,y,z) ] = d_{t}[ F(x,y,z) ]
rot[ B(x,y,z) ] = d_{t}[ D(x,y,z) ]

∯ [ F(x,y,z) ] d[(yz,zx,xy)] = G(x,y,z)
∯ [ D(x,y,z) ] d[(yz,zx,xy)] = S(x,y,z)

∯ [ F(x,y,z) ] d[(yz,zx,xy)] = ∭ [ div[ F(x,y,z) ] ] d[x]d[y]d[z]
∯ [ D(x,y,z) ] d[(yz,zx,xy)] = ∭ [ div[ D(x,y,z) ] ] d[x]d[y]d[z]

div[ F(x,y,z) ] = d_{xyz}^{3}[ G(x,y,z) ]

div[ D(x,y,z) ] = d_{xyz}^{3}[ S(x,y,z) ]

Ecuacions d'ona electro-magnétiques y gravito-magnétiques:

d_{t}[ div[ E(x,y,z)+B(x,y,z) ] ] = Lap[ E(x,y,z)+B(x,y,z) ] [o] (d_{t}[x]+d_{t}[y]+d_{t}[z])

d_{t}[ div[ J(x,y,z)+H(x,y,z) ] ] = Lap[ J(x,y,z)+H(x,y,z) ] [o] (d_{t}[x]+d_{t}[y]+d_{t}[z])

d_{t}[ div[ F(x,y,z)+D(x,y,z) ] ] = Lap[ F(x,y,z)+D(x,y,z) ] [o] (d_{t}[x]+d_{t}[y]+d_{t}[z])

d_{tt}^{2}[ E(x,y,z)+B(x,y,z) ] = Lap[ E(x,y,z)+B(x,y,z) ] [o] (d_{t}[x]^{2}+d_{t}[y]^{2}+d_{t}[z]^{2})

d_{tt}^{2}[ J(x,y,z)+H(x,y,z) ] = Lap[ J(x,y,z)+H(x,y,z) ] [o] (d_{t}[x]^{2}+d_{t}[y]^{2}+d_{t}[z]^{2})

d_{tt}^{2}[ F(x,y,z)+D(x,y,z) ] = Lap[ F(x,y,z)+D(x,y,z) ] [o] (d_{t}[x]^{2}+d_{t}[y]^{2}+d_{t}[z]^{2})