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# Assume (5.7.1)(5.7.6) are valid. Consider the one-dimensional wave equation with ISBN: 9780321797056 284

## Solution for problem 5.7.3 Chapter 5.7

Applied Partial Differential Equations with Fourier Series and Boundary Value Problems | 5th Edition

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Problem 5.7.3

Assume (5.7.1)(5.7.6) are valid. Consider the one-dimensional wave equation with nonconstant density so that c2(x) 2u t2 = c 2(x) 2u x2 . (a) Prove that eigenfunctions corresponding to different eigenvalues are orthogonal (with what weight?). (b) Use the Rayleigh quotient to prove that > 0. (c) Solve the initial value problem. You may assume the eigenfunctions are known. Derive coefficients using orthogonality.

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Chingiz Mardanov cm3283@drexel.edu Philadelphia, PA 19104 • chingiz@li.ru • 215-594-3163 Education Drexel University Philadelphia, PA Bachelor of Science in...

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##### ISBN: 9780321797056

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