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LAMat3 - Math 3353 Matlab Assignment 3 Due T Hagstrom 1...

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Math 3353 Matlab Assignment 3 - Due 11/02/09 T. Hagstrom 1. Consider the following transformation from P 6 P 6 : T ( p ) = - d 2 p dx 2 + 2 p i. Verify (on paper!) that T is a linear transformation. ii. Using the monomial basis for P 6 , { 1 , x, x 2 , . . . , x 6 } , build, in Matlab, the matrix representing T . Use the Matlab command null to verify that the matrix is invertible. iii. Use Matlab and the matrix constructed above to find p P 6 satisfying: - d 2 p dx 2 + 2 p = x 6 + x 4 + x 2 - 3 x Write out the polynomial, p , that you compute. 2. Consider an age-structured population model based on exisiting data for the US. We break the population into groups of 5 years. That is, x k = population aged 5 k - 5 to 5 k - 1 years We set x 21 to be the total number of people aged 100 or more. In a given year the population changes by the following processes: i. Births - x 1 is increased by the sum of the birth rates for each group mulitplied by the population in each group: k b k x k ii. Deaths - x k is decreased by the death rate for the group: - d k x k iii.
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