PHYS 112 Midterm: PHYS 112 IA State Exam1 solutionsx
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0 < t, 0 < x < 1, B( ) sin x exp( 2 2t) d . u(x, t) =z . 0: (25 points) state the eigenvalue problme for the di erential equation plus boundary conditions ut = 6uxx ux(0, t) = 0, ux( , t) + u( , t) = 0. 0 < t, 0 < x < , 0 < t: (25 points) solve the eigenvalue problem (that is, nd all eigenvalues and eigenfunc- tions, and show all steps): 0 < x < , x(0) = 0, x( ) = 0: (10 points) problems 2, 3, 4 correspond to the steps in solving an initial boundary value problem. Put them in the correct order. (no partial credit. )
