MAT 341 Final: MAT 341 Final Exam
31 Jan 2019
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7: find the solution of the laplace equation. U = 0, in the unit disc d1 r2, with boundary function u(1, ) = cos sin : the disc d1 r2 of radius 1 is completely insulated (0 temperature. The initial temperature distribution is u(r, , 0) = cos r. What is the steady-state temperature distribution: solve the wave equation for 0 < x < with boundary and initial conditions: T2 , u(0, t) = 0, u( , t) = 0, u(x, 0) = 2 sin 3x, T (x, 0) = 0: the motion of a string of length , xed at both ends and vibrating in a viscous medium is governed by the equation. T (the damped wave equation) with boundary conditions u(0, t) = 0, u( , t) = 0. Here k measures the viscosity of the medium (k = 0 is the standard wave equation) and we have set c = 1.
