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Pune University - SY BSc (Sem - I) MATHEMATICS - II (B), April 2010

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Total No. of Questions : 4] [Total No. of Pages : 2 [3717] - 102 P259 S.Y. B.Sc. (Sem. - I) MATHEMATICS (B) : Numerical Analysis (New Course) Paper - II (B) Time : 2 Hours] Instructions to the candidates : 1) All questions are compulsory. 2) Figures to the right indicate full marks. 3) Use of non - programmable calculator is permitted. [Max. Marks : 40 Q1) Attempt the following: [10] a) An approximate value of is given by 3.1427852 and it s true value is 3.14159265. Find absolute and relative error. b) Use Newton - Raphson method for evaluating 4 1 3 . c) Prove that - . d) If f(x) = e) Round - off following numbers to two decimal places. 1 , find f(a, b). x2 61.0561, 105.7845. f) Is it possible to solve the system of equations:3x + 2y = 5; 7x 5y = 8 by Gauss - Seidel iterative method? Justify. g) 2 Evaluate x3, take h = 1. h) Find the number of changes of signs of the polynomialf(x) = 2x7 6x4 + 8x3 15 = 0. i) State Sturm s theorem. j) Construct the divided difference table for the data. x: 1 f(x) : 21 1 15 2 12 P.T.O. 3

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Additional Info : S.Y. B.Sc. Mathematics (B) (Semister - I) : Numerical Analysis (Paper - II(B)) (New Course), Pune University
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