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Mathematics 325
Exam I
Name:
.
Summer 20 10
1
.(25 pts.) (a) Find the characteristic curves of
yu, xu,
=
0 in the
xy

plane.
(b) Sketch and identify two characteristic curves of this partial differential equation.
(c) Write the general solution of this partial differential equation in the
xy

plane.
(d) Find the solution of this partial differential equation which satisfies
u
(x,
0)
=
x6
for all real
x
.
(e) In what region of the
xy

plane is the solution in part (d) uniquely determined?
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View Full Document 2.(25 pts.) An elastic string is held fixed at the endpoints and plucked. Assuming that air exerts
a
resistance at each point of the string which is proportional to the string's velocity at that point, give a
careful derivation of the partial differential equation that governs the small vibrations of the string.
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View Full Document 3.(25
pts.) Classify the following second order partial differential equations as hyperbolic, parabolic,
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This note was uploaded on 01/11/2011 for the course MATH Math 325 taught by Professor Davidfrow during the Fall '10 term at Missouri S&T.
 Fall '10
 DavidFrow
 Math, Equations

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