For this problem:
We have this graph:
What I am confused is what should $u'(0)$ and $u'(1)$ be?
1) For $u'(0)$ , the solution is $u'(0) = \frac{u_2-u_1}{\Delta x}$ , but why is it not $u'(0) = \frac{u_1-u_0}{\Delta x}$???
2) Same thing as $u'(1)$ , the solution is $u'(1) = \frac{u_4-u_3}{\Delta x}$ , but why is it not $u'(0) = \frac{u_5-u_4}{\Delta x}$???