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exam2

# exam2 - Second Midterm November 18th 2009 NAME(Please print...

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Second Midterm November 18th, 2009 NAME (Please print) Question Score 1 2 3 4 Total points 100 Instructions: 1. Each problem is worth 25 points. 2. No calculators, computers, notes, books are permitted. 3. Do all computations on the examination paper. You may use the backs of the pages if necessary. Make your work readable . 4. To receive full credit put answers inside the boxes (when applicable). 5. Please signify your adherence to the honor code: I, , have neither given nor received aid in completion of this examination. 1

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QUESTION 1 Score (25 Points) Find the eigenvalues and eigenfunctions of the self-adjoint boundary problem: X 00 + λX = 0 X (0) - X 0 (0) = 0 X (1) - X 0 (1) = 0 2
QUESTION 1 3

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QUESTION 2 Score Consider the Laplace equation: u xx + u yy = 0 u ( x, 0) = f ( x ) u ( x, 1) = 0 u (0 , y ) = 0 u (1 , y ) = 0 1. (10 points) Write down the boundary problem and the initial value problem that X ( x ) and Y ( y ) have to solve when using the method of separation of variables to find the fundamental solutions. 4
QUESTION 2 2. (15 points) Solve the Laplace equation: u xx + u yy = 0 u ( x, 0) = 0 u ( x, 1) = f ( x ) u (0 , y ) = 0 u (1 , y

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exam2 - Second Midterm November 18th 2009 NAME(Please print...

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