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# Reconsider Exercise 9.6.1 subject to the periodic boundary conditions that the

ISBN: 9780321797056 284

## Solution for problem 9.6.3 Chapter 9.6

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

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

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Problem 9.6.3

Reconsider Exercise 9.6.1 subject to the periodic boundary conditions that the eigenvalue splits. This means that if = 0, there is one eigenfunction for each eigenvalue, but as 0, two eigenvalues will approach each other (coalesce), yielding eigenvalues with two eigenfunctions. [Hint: It is necessary to consider a linear combination of both eigenfunctions ( = 0). For each eigenvalue, determine the specific combination of these eigenfunctions that is the unique eigenfunction when = 0.]

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Limits and Discontinuity Notes Limits of sequences: 1/2 , k approaches ∞, and the fraction approaches 0. 0 is the limit as k approaches ∞. (2 -1)/2 , k approaches ∞, and the fraction approaches 1. 1 is the limit as k approaches ∞. Limits of average rates of change: finding final instantaneous velocity, calculate the rate of change over the last...

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Reconsider Exercise 9.6.1 subject to the periodic boundary conditions that the

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