Life science math homework notes

So that whole system of short hands of PDE calculations is called the Einstein notation:
http://en.wikipedia.org/wiki/Einstein_notation

The Levi-Civita symbols, also called permutation or antisymmetric symbols, is actually the εijk part:
εijk
=+1 if (i,j,k)=(1,2,3), (2,3,1)or (3,1,2)
=-1 if (i,j,k)=(3,2,1), (1,3,2)or (2,1,3)
=0 if i=j or j=k or k=i
http://en.wikipedia.org/wiki/Levi-Civita_symbol

While the δij part is the kronecker delta:
δij =1 when i=j
else, δij =0
http://en.wikipedia.org/wiki/Kronecker_delta

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For info on the last question (caution, very long):
http://en.wikipedia.org/wiki/Maxwell_equations

For (i) in the 2nd question, it wants us to explain the " Euler equation", however, the seems to be tens of hundreds of " Euler equation", and I can't find the right one. Please do tell me if you can.
(∂v/∂t)+ v・∇v = -(1/ρ)∇p - ∇φ

http://en.wikipedia.org/wiki/Euler_equation