Math 641-600 Suggested Problems (Fall 2010)
Suggested Problems for Chapter 4 - These
are not to be handed in.
- Section 4.1: 5, 8
- Section 4.2: 2, 4
- Section 4.3: 2, 3, 5
- Let Lu = −(xu′ )′, D(L) := {u, Lu ∈
L2[1,2], u(1) = u(2) = 0}.
- Show that L is self adjoint and positive definite with respect to
the inner product for L2[1,2].
- Find the Green's function for L.
- Show directly i.e., without quoting Theorem 4.7 by
using the Green's function that the eigenfunctions of L are complete
in L2[1,2].
Updated 12/5/10.