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exam1su10 - Mathematics 325 Exam I Summer 20 10 Name: ....

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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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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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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.

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exam1su10 - Mathematics 325 Exam I Summer 20 10 Name: ....

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