Problem:
1. Eigenvalues, eigenfunctions and modified Green's function.
(a) Find the eigenvalues and eigenfunctions of
- u" = λu, -1 < x < 1; u'(1) - u (1) = 0, u'(-1) + u (-1) = 0
Show that there is precisely one negative eigenvalue, that zero is an eigenvalue, and that there are infinitely many positive eigenvalues.
Show graphically how the eigenvalues are determined.
(b) Find the modified Green's function when λ = 0.