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FINAL EXAM - Department of Mechanical Engineering The...

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Department of Mechanical Engineering The University of Texas at Austin ME 218 Engineering Computational Methods Final Examination Fall 2008 Instructor: Prof. Dragan Djurdjanovic December 10, 2008 (9 am – 12 pm) Student Name:_____________________ Student EID:___________________ Lab Section Number (or time):___________________ I have neither given nor received any unauthorized aid on this exam, nor have I concealed any violations of the honor code. Signature:____________________ Note: There are 4 problems. Each problem carries 25 points. There are 100 points in total for you to win. GOOD LUCK!!! 1
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PROBLEM 1: Simultaneous Nonlinear Equations (25 POINTS) Plot the following set of nonlinear equations, it is judged that a solution is near the point =- x0 . 2 3 , =- . y0 19 7 . This initial guess needs to be refined. Select an appropriate method and perform 3 iterations of that method to refine this initial guess. 3 x 3 – 4 x – y = -7 x 2 – y = 25 Please use 4 decimal digits in your answers and note the formula for inversion of a 2 by 2 matrix  (you may need it) - = - - - abcd 1 1ad bcd b ca 2
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