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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.
 Fall '08
 BELL,D

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