Originally Posted by
mathswannabe okay this is a docarmo question asking if x(u,v) = (u+v,u-v,4uv) parameterizes the graph z=x^2 - y^2.
How do we show that it does this.
Is the question asking does the parameterization give you a regular surface that is the subset of the graph? Considering the next question says 'what parts of the surface does it cover?'
If my assumption is right.... i guess we just have to show that its 1:1 (dont need to worry about surjectivity since it only covers a part of the surface), that its cts and its inverse is cts... that its twice differentiable and that the differential is injective....
Using a theorem in docarmo, x is 1:1 implies its inverse is cts...
My big question is though:
HOW DO WE GO ABOTU SHOWING THIS PARAMETERIZES THE WHOLE SURFACE?!?
any help here would be so great!