Introduction to Numerical AnalysisMath 104A, Winter 2009Instructor:Carlos J. Garc´ıa-CerveraMarch 17th, 2009Answer the following 8 questions. Show all your work for full credit. You mustinclude 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 5Please go on to the next page. . .
Math 104AFinal ExamWinter 20091. (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