0The function of two variables, level curves, geometrical meaning
graph of f is the set of all points (x,y,z) in such that z=f(x,y) and (x,y) is in the domain of a function
The graph of the function of two variables is interpreted geometrically as the surface in space.
The level curves are Scaler fields F(X, Y)=C where c is constant.
level curves f(x,y)=c are traces of graph of function f in horizontal plane z=c projected down to XY-plane
The level curves of a function f of two variables are the curves with equations f (x,y)=c
