Consider the eigenvalue problem d2 dx2 + = 0, subject to d dx (0) = 0 and d dx (L) +
Chapter 5, Problem 5.8.3(choose chapter or problem)
Consider the eigenvalue problem d2 dx2 + = 0, subject to d dx (0) = 0 and d dx (L) + h(L) = 0 with h > 0. (a) Prove that > 0 (without solving the differential equation). *(b) Determine all eigenvalues graphically. Obtain upper and lower bounds. Estimate the large eigenvalues. (c) Show that the nth eigenfunction has n 1 zeros in the interior.
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