I'm reading a graphics book and it talks about BRDFs being the ratio between differential outgoing radiance and differential irradiance. The formula it gives is f(l, v) = dL(v)/dE(l) Where l is the light vector and v is the outgoing direction vector, and L is outgoing radiance and E is incoming irradiance.
But then the book says that for non area lights like directional and point lights, the BRDF can be expressed without differentials: f(l, v) = L(v) / E(l). How is this possible? The first formula seems to be a derivative, how do we get to this formula? What is the difference between non area and area lights that would allow us to arrive at this simplification?