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Unformatted text preview: CAAM 336 Â· DIFFERENTIAL EQUATIONS Examination 1 Posted Friday, 17 October 2008. Due no later than 5pm on Tuesday, 21 October 2008. Instructions: 1. Time limit: 4 uninterrupted hours . 2. There are three questions worth a total of 105 points. (Any scores above 100 will be regarded as bonus.) Please do not look at the questions until you begin the exam. 3. You may not use any outside resources, such as books, notes, problem sets, friends, calculators, or MATLAB. 4. Please answer the questions thoroughly and justify all your answers. Show all your work to maximize partial credit. 5. Print your name on the line below: 6. Time started: Time completed: 7. Indicate that this is your own individual effort in compliance with the instructions above and the honor system by writing out in full and signing the traditional pledge on the lines below. 8. Staple this page to the front of your exam. CAAM 336 Â· DIFFERENTIAL EQUATIONS 1. [27 points: 7 points for (a); 5 points each for (b), (c), (d), (e)] Consider the differential equation with homogeneous Neumann boundary conditions u 00 ( x ) = f ( x ) , u (0) = u (1) = 0 , which we associate with the linear operator L defined by Lu = u 00 on the space C 2 N [0 , 1] = { v âˆˆ C 2 [0 , 1] : v (0) = v (1) = 0 } . (a) Compute all eigenvalues { Î» n } and eigenfunctions { Ïˆ n } of L ....
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 Fall '09
 Tompson
 Linear Algebra, Eigenvalue, eigenvector and eigenspace, Orthogonal matrix, Eigenfunction, inner product, best approximation

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