Final_Winter2009_TakeHome - Introduction to Numerical Analysis Math 104A Winter 2009 Instructor Carlos J Garc a-Cervera March 17th 2009 Answer the

# 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. . . Math 104A Final Exam Winter 2009 1. (10 points) An amount ofP1dollars is put into an account at the beginning of years 1,2, . . . , N1.It is compounded annually at a rate orr(e.g.,r= 0.05 means a 5 percent rate of interest).At the beginning of yearsN1+ 1, . . . , N1+N2, a payment ofP2dollars is removed from theaccount. After the last payment, the account is exactly zero. The relationship of the variablesisP1(1 +r)N1-1=P21-(1 +r)-N2.IfN1= 30,N2= 20,P1= 2000, andP2= 8000, then what isr?2. (10 points) Consider the following iterative method to solvef(x) = 0:xn+1=g(xn),whereg(x) =x-f(x)f0(x)-12f00(x)f0(x)f(x)f0(x)2.(a) (5 points) Does the method converge? What is the rate of convergence of the method?Justify your answer.(b) (5 points) Find, using this method, and to within 10-10, the solution toe-x= sin(x)located in the interval [0,1].3. (10 points) Find the coefficientsa0,a1  • • • 