[Important] L16 Clarification
I don not follow how you plug Eq 16.10 into Eq 16.7. The integrals do not match at all anywhere.
If I plug c(x)(from Eq. 16.7) directly into Eq. 16.10 I do not see how you resolved the arising double integral and how you treated the partial derivative (
\partial U / \partial x). Is there a c(x) term missing in eq 16.17 or are there some other steps that you have omitted. If so could you help me understand how you got this result? Because it is proving hard to follow this lecture in order to solve Q3 in HW4
Also there seems to be a typo in page 151
should it be here 'we plug Eq. 16.10 into Eq 16.13' for the second integral on the RHS?