Differential Equations Lecture Work Solutions 275

Differential Equations Lecture Work Solutions 275 - 7.3...

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Unformatted text preview: 7.3 7.3.1 Second Order Wave Equation Infinite Domain Problems 1. Suppose that u(x, t) = F (x − ct). Evaluate ∂u (x, 0) ∂t ∂u (0, t) b. ∂x a. 2. The general solution of the one dimensional wave equation utt − 4uxx = 0 is given by u(x, t) = F (x − 2t) + G(x + 2t). Find the solution subject to the initial conditions − ∞ < x < ∞, u(x, 0) = cos x − ∞ < x < ∞. ut (x, 0) = 0 3. In section 3.1, we suggest that the wave equation can be written as a system of two first order PDEs. Show how to solve utt − c2 uxx = 0 using that idea. 275 ...
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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