Vocabulary

[JeffM]

Suppose I have \(\displaystyle z = f(x,\ y),\ f_x(x,\ y) = g(x),\ f_y(x,\ y) = h(y) \implies dz = g(x) * dx + h(y) * dy\).

Is there a name for such a function? Is there a name for the relationship between the x and y variables? Are x and y orthogonal variables?

 

[Romsek]

Suppose I have \(\displaystyle z = f(x,\ y),\ f_x(x,\ y) = g(x),\ f_y(x,\ y) = h(y) \implies dz = g(x) * dx + h(y) * dy\).

Is there a name for such a function? Is there a name for the relationship between the x and y variables? Are x and y orthogonal variables?

These are called additively separable functions. If you work it through you'll see that f(x,y) = u(x) + v(y) where u and v are the indefinite integrals of g and h respectively.

http://calculus.subwiki.org/wiki/Additively_separable_function

 

[JeffM]

These are called additively separable functions. If you work it through you'll see that f(x,y) = u(x) + v(y) where u and v are the indefinite integrals of g and h respectively.

http://calculus.subwiki.org/wiki/Additively_separable_function

Thank you for your helpful response.