Final_Winter2009_TakeHome

Final_Winter2009_TakeHome - Introduction to Numerical...

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Introduction to Numerical Analysis Math 104A, Winter 2009 Instructor: Carlos J. Garc´ ıa-Cervera March 17th, 2009 Answer the following 8 questions. Show all your work for full credit. You must include your computer programs. Follow the guidelines for presentation of results . Name: Due on Tuesday March 17th, before 4pm. Problem 1: out of 10. Problem 2: out of 20. Problem 3: out of 10. Problem 4: out of 25. Problem 5: out of 20. Problem 6: out of 20. Problem 7: out of 35. Problem 8: out of 40. Total: out of 170. THESE SHEETS ARE TO BE HANDED IN WITH YOUR EXAM. Page 1 of 5 Please go on to the next page. . .
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Math 104A Final Exam Winter 2009 1. (10 points) An amount of P 1 dollars is put into an account at the beginning of years 1 , 2 , . . . , N 1 . It is compounded annually at a rate or r (e.g., r = 0 . 05 means a 5 percent rate of interest). At the beginning of years N 1 + 1 , . . . , N 1 + N 2 , a payment of P 2 dollars is removed from the account. After the last payment, the account is exactly zero. The relationship of the variables is P 1 ± (1 + r ) N 1 - 1 ² = P 2 ± 1 - (1 + r ) - N 2 ² . If N 1 = 30, N 2 = 20, P 1 = 2000, and P 2 = 8000, then what is r ? 2. (10 points) Consider the following iterative method to solve f ( x ) = 0: x n +1 = g ( x n ) , where g ( x ) = x - f ( x ) f 0 ( x ) - 1 2 f 00 ( x ) f 0 ( x ) ³ f ( x ) f 0 ( x ) ´ 2 . (a) (5 points) Does the method converge? What is the rate of convergence of the method? Justify your answer.
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This note was uploaded on 12/26/2011 for the course MATH 104a taught by Professor Staff during the Fall '08 term at UCSB.

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Final_Winter2009_TakeHome - Introduction to Numerical...

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