Thread: First and second fundamental forms. Find the Coefficients.

0(u,v) = ( u - (u^3)/3 + u(v^3), v - (v^3)/3 + v(u^2), u^2 - v^2 )

I Need to find First fundamental form co-efficiants E F G
And Second Fundamental From Co-Efficients e f g

I have a book here that shows me but i cant figure it out for this question using the way the book shows. I need someone to talk me through the method. Thanks

For 1st FF I get

E = (1 - u^2 +u)^2 + (2uv)^2 + + (2u)^2

F = (1-u^2 + u)(2uv) + (2uv)*(1-v^2 + v) + (2u)(-2v)

G= (2uv)^2 + (1-v^2 + v)^2 + (-2v)^2

Is this correct