MATH 348 - April 14, 2008 NAME:
Exam II - 50 Points - 50 minutes SECTION:
In order to receive full credit, SHOW ALL YOUR WORK. Full credit will be given only if all
reasoning and work is provided. When applicable, please enclose your final answers in boxes.
1. (10 Points) Conceptual Questions.
Suppose that we have the graph of the initial condition u(x, 0) = f(x):
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(a) Assume that fis the initial temperature for a homogenous heat problem with boundary conditions,
ux(0, t) = 0, ux(1, t) = 0. Describe the physical meaning of these boundary conditions and graph the
approximate temperature profile for t→ ∞.
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y
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(b) Assume that fis the initial displacement of an elastic string modeled by the homogenous wave equation
subject to boundary conditions u(0, t) = 0, u(1, t) = 0. Describe the physical meaning of these boundary
conditions and describe time-dynamics of the points, P1and P2, on this elastic string assuming that
the string has no initial velocity.
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