Discuss the different types of errors in Numerical Methods.

Explain the 'pseudocode' and 'floating point numbers'.

2. What is the importance of optimization methods in Civil Engineering? Explain with the help of a suitable example.

3. Explain the following:

Trapezoidal Rule, and

Ill-conditioned system of equations.

Use the Newton-Raphson method to determine a root of the equation x^3 -2x correct to three decimal
places.

Develop a computer algorithm for finding the roots of using the Bisection Method.

5. Solve the equations,

2x 3y Z 9

x 2y+ 3z 6

3x+ 2z 8

by LU decomposition method.

6. Given the points and satisfying the function y sin x x determine the value of using cubic spline method.

Explain Newton's Forward Interpolation formula for any function y

Define eigen values, eigen vectors and conditions of convergence.

8. Use Runge-Kutta method of fourth order to solve:

dy/dx y^2 with at x =0·2, 0·4 and 0·6.

9. Explain the unconstrained optimization problem of non-linear programming.

10. Discuss the differences between linear and non-linear programming problems.