Math 641-600 Fall 2011
Current Assignment
Assignment 9 - Due Friday, 12/2/2011
- Read sections 4.1,4.2
- Do the following problems.
- Section 3.6: problem 1, page 130.
- Section 3.6: problem 4, page 131.
- Section 3.6: problem 5, page 131.
- Consider eigenvalue problem y′′ = - λ y. with
boundary conditions y(0)=0, y(1)+y′(1) = 0. Show that the
eigenvalues satisfy the equation tan(λ1/2) +
λ1/2 = 0 and the eigenfunctions have the form
φ(x) = sin(λ1/2x). Show that the
eigenfunctions are a complete set in L2[0,1] by
converting the problem to one of the form
λ−1 u = Ku for an appropriate kernel. (Hint:
to convert the problem, use variation of parameters.)
- Section 4.1: Problem 1(c), page 171.
Updated 11/23/2011.