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Posted By: aravindsri Member Level: Gold Posted Date: 02 Jun 2008
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2005 Indira Gandhi National Open University (IGNOU) B.Tech Civil Engineering ET302 (A) Computer Programming & Numerical Analysis December 2005 Question paper
IGNOU ET302 (A) Computer Programming & Numerical Analysis December 2005
B.Tech. Civil (Construction Management) /
B.Tech. Civil (Water Resources Engineering)
Term-End Examination
December, 2005
ET-302(A) : COMPUTER PROGRAMMING & NUMERICAL ANALYSIS
Time: 3 hours
Maximum Marks: 70
Note : Attempt any five questions. All questions carry equal marks. Use of calculator is allowed.
1. (a) Perform three iterations of the Regula - Falsi method to find the root of the equation x4 - x - 10 = 0 in the interval [1, 2]. Assume suitable initial approximations.
(b) Consider the following system of equations :
4x - y + z = 7
4x - 8y + z = - 21
-2x + y + 5z = 15
Perform only four iterations of Jacobi iteration or Gauss - Seidel itertion method for solving the equations. Assume (xo, yo, zo) = (1,2,2) to start with. (7,7)
2. (a) Use the LU decomposition method to solve the system of equations :
x + y + z = 1
4x + 3y - z = 6
3x + 5y + 3z = 4
(b) Find the dominant eigenvalue and the corresponding eigenvector correct to two decimal places of the matrix
2 -1 0
A = -1 2 -1
0 -1 2
Using the power method and carry out four iterations. (7,7)
3. (a) Verify the equivalence of the following relations :
(i) ?2 cos (2x) = -4 sin2h cos (2x + 2h)
(ii) (?2/E) x3 = 6x
(iii) E (2µd - ?) = ?
(b) Using Muller's method, find a root of the equation x3 - x2 - x - 1 = 0 which lies between 3 and 4 correct to 3 decimal places. (6,8)
4. (a) The values of a polynomial of degree 5 are tabulated below. If f(4) is known to be in error, find its correct value.
x: 2.5 3.0 3.5 4.0 4.5 5.0 5.5
f(x): 4.32 4.83 5.27 5.47 6.26 6.79 7.23
(b) In the table below. the values of y are consecutive terms of a series of which 43 is the 6th term. Find the first and the tenth terms of the series.
x: 3 4 5 6 7 8 9
y: 4.8 8.4 14.5 23.6 36.2 52.8 73.9
5. (a) Solve the following system of linear equations with Gaussian elimination method :
2x1 - 2x2 + 5x3 = 6
2x1 + 3x2 + x3= 13
-x1 + 4x2 - 4x3 = 3
(b) Find Lagrange's interpolating polynomial for the following data. Also obtain the value of f(2) using polynomial.
x 0 1 4 5
f(x) 8 11 68 123
6. (a) Using second order Taylor series method upto the terms of h2 solve the equation, dy/dx = 3x + y/2; y(0) = 1. Find y(0.4) taking h=0.2.
(b) Solve the differential equation
dy/dx = 1/x2 - y/x - y2, y(1) = -1 by Runge - Kutta method for x = 1 to x = 5/3 in steps of h = 1/3 by carrying out calculation in two steps. (7, 7)
7. (a) The sum of the squares of the first n natural numbers is given by
n(n+1)(2n+1)
s = ----------------
6
Write a program that will find s for n = 10 (10) 250, i.e., n = 10, 20, 30, ....., 250
(b) Using logical IF statements, write a program that calculates and prints
f(x) = {3x + 5x3 for 4.3=x<9.1
{6x + 8x2 for 9.1=x<15.5
for x varying from 5.0 to 15.0 in steps of 0.5 (7, 7)
8. (a) The values of x are to be tabulated from the formula
x = (sin t e-2t + log t) / (5t - cos t)
for t = 1.0 to 5.0 in steps of 0.1 Write a program to compute and print x for each value of t in the given range.
(b) Write a program to compute ?n. Test for n = 0, 1 and 3. (7,7)
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