Final-sample

Final-sample - MAE 107 Computational Methods in Engineering...

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1 MAE 107 Computational Methods in Engineering Spring 2008 Sample Final Exam Guidelines: The exam will be closed book and closed notes, except that one page (both sides of a standard letter-size page) of handwritten notes is allowed . No calculators or computers will be allowed. Please write out your solutions neatly, including all necessary intermediate steps, and indicate clearly all final answers. 1. ( 20 points ) Consider a method for finding the root of the equation 0 ) ( = x f . (a) Derive a method for solving this equation that is similar to Newton’s method but that uses the first three terms of a Taylor series expansion instead of the first two terms. (b) Prove that this method has a cubic rate of convergence. 2. ( 20 points ) Consider the coefficient matrix 21 0 12 1 01 2 =− A a. Use Gaussian elimination to construct the LU decomposition of A . b. Use this LU decomposition to construct the inverse of A .

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This note was uploaded on 10/11/2011 for the course MAE 107 taught by Professor Rottman during the Summer '08 term at UCSD.

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Final-sample - MAE 107 Computational Methods in Engineering...

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