The following two definitions are given in my lecture notes:
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 some rectangular domain then the differential form Mdx + Ndy is exact in R
if and only if ∂m/∂y = ∂n/∂x in 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?