The following two definitions are given in my lecture notes:

First.

Let u : R x R --> R be a function with continuous partial derivatives and let y: R--->R be differentiable

What does u: R x R ---> R mean?

and what does y: R--->R mean

secondly, to test if a function is exact, we have:

If M and N are continuous and have continuous first order partial derivatives in somerectangular domainthen the differential form Mdx + Ndy is exact inRif and only if

∂m/∂y =∂n/∂xin R

I understand everything up until the "Rectangular domain". What is that supposed to tell me? How do I know if a domain is rectangular?

Thanks.