Example 2 — p. 91
There is some confusion with regard to example 2, p. 91 in the
text. This stems from the connection between the solution to
minimizing
∫01 (u′) 2dx, u(0) = a,
u(1) = b
and solving the boundary value problem (BVP) u′′ = 0, u(0)
= a, u(1) = b. The point the author is making is that the solution to
the BVP is precisely the minimizer. As he states, this follows from
the calculus of variations (chapter 5), and is not derived in
the example. The example itself only deals with approximating the
minimizer, and gives no justification for the connection to the BVP.