I'm reviewing this document:

http://ocw.mit.edu/courses/mathemati...18_03S10_i.pdf

The short story is that is the weight function (solution to the associated homogeneous equation) of some generic equation . We want to break the interval between into smaller intervals, and define so that over the interval it's a constant function. This means that .

I get everything until page 3 equation (8). If is the weight function for , then I would think that for , the weight function would just be (restricted to the interval). I don't understand why we need to amplify this by .

(I forgot to include a part about Leibniz's Formula but I'm too tired.)