RTU Previous Year Question Papers BE
Computer Application in Civil Engineering Feb 2011
1.a) Find the roots of equation x3 – x – 4 = 0 correct to three decimal places using Newton-Rap son Method.
b) Write the algorithm for finding, roots of a non linear equation using Bisection Method.
a) F ind the truncation error for e x at x — and x = – when we use
i) First three terms
ii) First four terms.
b) Find the real root of / (jc) = x3 – 2x – 5 = 0
by Bisection Method.
2. a) Solve the following system of equations by Gauss-Seidal Method
27 x + 6y – z = 85 6jc+ 15y + 2z = 12 x +y + 54z =110
b) Write the algorithms for solving the Linear simultaneous equations using triangularizing method.
(a)What do you mean by Linear independent simultaneous equations?
(b) Solve the following equations:
x + 2y + 3z = 1 2x + 3y + 2z = 2 3x + 3y + 4z = 1 by Gauss Elimination Method.
(a)Write a short note on “Regression Analysis”.
(b)Fit a second degree parabola to the following data taking x as the independent variable.
(a)Write a short note on “Numerical Analysis.
(b)The ordinates of the normal curve are given by the following table.
|v: j •||.3989||.3910||.3683||.3332||.2897|
(i) y (0-25) (ii) y (0.62)
4 (a)Compute the values of by the
i) Trapezoidal rule
ii) Simpson’s ~ rule and compare your result with the true value.
(b)What is the use of “Numerical Integration” to find area of a curve.
a) Evaluate by Simpson’s rule with six intervals.
b) A curve is drawn to pass through the points given by the following table
Estimate the area bounded by the curve, x – axis and the lines x = 1 and x = 4.
5. a) Use Euler’s modified method with one step to obtain the value ofy at x = 0.1 when ^j-=x2 +y with x = 0, y = 0.94.
b) Explain any one method used for numerical solution of partial differential equation.
Use Runge-Kutta fourth order method to solve £:=-2V with x0 = 00= 1