Can anybody help with this:
I have . How to extract u,v as functions from x,y, i.e. to get u(x,y) and v(x,y)?
Right, so you don't actually need the explicit formula.
For example, to find and .
Take the partials of the equations directly (independent variables are ):
Note that and .
Solve this system of linear equations at the given point for .
Similar process for other derivatives.
Note you do need to solve for u and v at the point , and you use these values when evaluating things like sin(u).