Download OU B.Sc 2016 April 3rd Year 2020E Mathematics Question Paper

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Code No. 2020/ E

FACULTIES OF ARTS AND SCIENCE

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B.A./ B.Sc. I Year Examination, March / April 2016

Subject : MATHEMATICS

Paper — IV (a)

Numerical Analysis

Time : 3 hours Max. Marks : 100

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Note : Answer Six questions from Part-A & Four questions from Part-B.

Choosing atleast one from each Unit. Each question in Part-A carries 6 marks and in Part-B carries 16 marks.

Part— A (6 X 6 = 36 Marks)

Unit -1

1. If u=5xy²/Z³ then find maximum relative error in u given that ?x = ?y = ?z =0.001, x=y=z=1.

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2. Explain bisection method of finding a real root of f(x) = 0.

Unit - II

1. Derive Lagrange’s formula.
2. Define the operators ?, ?, E and d show that i) ?=?E=dE^½ ii) µ=½(E^½+E^-½)

Unit - III

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1. Explain the method of fitting a straight line to the given data using the principle of least squares.
2. Evaluate ?₁^1.2 (e^-x) dt using Trapezoidal rule with 8 strips.

Unit - IV

1. Apply Euler's method to compute y(0.4), y(0.6) given that dy/dx =x+vy, y(0)=0 with h=0.2.
2. Solve the following system of equation using Jacobi's iterative method 10x +2y +2z=9, 2x + 20y - 2z = -44, -2x + 3y + 10z = 22.

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Part— B (4 X 16 = 64 Marks)

Unit -1

1. a) Find the real root of x³ - x - 1 = 0 upto three decimal places using bisection method. b) Find a double root of x³ - 3x² - 4 = 0 by generalized Newton’s method.

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Code No. 2020 / E

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-2-

1. a) Using Newton Raphson method find a root of x⁴ - x - 10 = 0. b) Calculate the value of v102 - v101 correct to four decimal places.

Unit- II

1. a) Find the cubic polynomial which takes the following values. y(0) =1, y(1) = 0, y(2) = 1, y(3) = 10, hence obtain y(4). b) Prove that ?ⁿu_x =u_x+n - ⁿC₁u_x+n-1 +ⁿC₂u_x+n-2 +...+(-1)ⁿu_x.
2. a) Derive Newton’s forward difference interpolation formula. b) Using Newton’s forward difference formula, find the sum S_n=1³+2³+3³+...n³.

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Unit - III

1. a) Derive Simpsons 1/3 rule and find error in it. b) Find the value of ?₃⁷ xz logx dx by taking 8 strips using Boole’s rule.
2. a) Using Trapezoidal rule find the value of ?₀^p/2 v(cos?) d? by dividing interval into 6 parts. b) Fit a straight line to the following data :

Unit - IV

1. a) Solve the following systems of equations using Gauss elimination method 2x+y+z=10, 3x+2y +3z=18, x+ 4y + 9z = 16. b) Find the value of y for x = 0.1 by Picard’s method given that dy/dx = (y-x)/(y+x), y(0)=1.

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2. a) Use Runge-Kutta's method of fourth order to compute y(0.1), y(0.2) given dy/dx = vxy, y(1)=1. b) Use Taylor's series method to find y(0.1) correct to four decimal places if y(x) satisfies y' = x-y², y(0)=1.

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