MATH348 - April 11, 2011 NAME:
Exam II - 50 Points
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. For the following questions assume that we are considering the physical
problem on a bounded domain, xโ[0,1].
(a) Write down the heat and wave equations and also any initial conditions needed for unique solutions.
(b) Assume that the following graph is the initial temperature for a homogeneous heat problem with bound-
ary conditions, ux(0, t) = 0, ux(1, t) = 0. Describe the physical meaning of these boundary conditions
and graph the temperature profile for tโ โ.
6
-๎๎๎๎๎
@
@
@
@
@
r
x= 1
r(x, y)=(.5,1)
y
x
(c) Assume that the following graph is the initial displacement of an elastic string modeled by the homo-
geneous 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.
6
-๎๎
๎@@@@@๎๎
๎r
r
r
x= 1P2
P1
y
x
1
