Consider the eigenvalue problem 2 + = 0 x (0, y)=0, (x, 0) = 0 x(L, y)=0, (x, H)=0. *(a)
Chapter 7, Problem 7.4.1(choose chapter or problem)
Consider the eigenvalue problem 2 + = 0 x (0, y)=0, (x, 0) = 0 x(L, y)=0, (x, H)=0. *(a) Show that there is a doubly infinite set of eigenvalues. (b) If L = H, show that most eigenvalues have more than one eigenfunction. (c) Show that the eigenfunctions are orthogonal in a two-dimensional sense using two one-dimensional orthogonality relations.
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