32 + 42 = 52, 52 + 122 = 132, and 82 + 152 = 172= F=dAF=dA
dF=0dF=0
d⋆F=⋆J
Fab=2∇[aAb]Fab=2∇[aAb]
∇[aFbc]=0∇[aFbc]=0
∇aFab=
∇⋅B⃗=0∇⋅B→=0
∇⋅E⃗=4πρ∇⋅E→=4πρ
∂B⃗∂t=−∇×B⃗∂B→∂t=−∇×B→
∂E⃗∂t=+∇×B⃗−4πJ⃗.
∇⋅v⃗=∂vi∂xi∇⋅v→=∂vi∂xi
and the curl is defined as
(∇×v⃗)i=ϵijk∂vk∂xj.
∇⋅v⃗=∂vx∂x+∂vy∂y+∂vz∂z∇⋅v→=∂vx∂x+∂vy∂y+∂vz∂z
and curl is defined as
(∇×v⃗)z=∂vy∂x−∂vx∂y
= meaning of life 42
