Help with understanding taylor approximation

  • Thread starter MaxManus
  • Start date
1. The problem statement, all variables and given/known data
I'm reading about fluid mechanics and in one of the examples they have approximated the velocity field. The field is two dimensional u = (u,v)
I have never seen this before so cold someone tell me what it is called so I can look it up?
The notes I am reading are hand written so there may be small mistakes, but it seems likes some of the ts are primed.

u = u(x,y,t)

3. The attempt at a solution

u(0,0,t) = u(o,o,t) + [tex]\int_0^t[/tex]u(0,0,t')dt'[[tex]\nabla[/tex]u]x = 0
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