HW#5 - , c (0) = c (1) = 0 . 5. Suppose you are trying to...

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ChBE 521 Homework 5 due Wednesday, October 12 1. Beers 3.A.2 2. Beers 3.A.3 3. Beers 3.B.4 4. Consider the boundary value problem D d 2 c dx 2 = 0 , c (0) = c (1) = 0 . The eigenvalues for this equation are λ n = - n 2 π 2 , n = 1 , 2 , 3 , . . . and the eigenfunctions are φ n ( x ) = 2 sin( nπx ) , n = 1 , 2 , 3 , . . . . In other words, D d 2 φ n dx 2 = λ n φ n , φ n (0) = φ n (1) = 0 . (a) How do the numerically calculated eignvalues and eigenvectors com- pare with these results? To calculate the eigenvalues and eigenvec- tors, apply finite differences to the problem? (b) Suggest how one can use the eigenvalues and eigenvectors (eigenfunc- tions) to solve the problem D d 2 c dx 2 = f ( x )
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Unformatted text preview: , c (0) = c (1) = 0 . 5. Suppose you are trying to fit the equation y = θ 1 x 1 + θ 2 x 2 to data where the variables x 1 and x 2 are the experimental inputs (i.e. you control them) and y is the output (i.e. determined by x 1 and x 2 ). (a) How would you assign confidence intervals to your estimates for θ 1 and θ 2 ? (b) How would you choose values for x 1 and x 2 to get the most accurate estimates for θ 1 and θ 2 . Justify your answer. 6. Determine for what values of c , if any, x 2 + y 2 + z 2 ≥ c ( xy + yz + zx ) 1...
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This note was uploaded on 11/30/2010 for the course CHBE CHBE521 taught by Professor Chrisrao during the Spring '10 term at University of Illinois, Urbana Champaign.

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