Draw a flow chart to read 15 numbers and find out its mean and variance.

Write a program to read two matrices A and both are square matrices, and check whether A or not.

Write the arithmetic statement functions for the following in FORTRAN:





Explain the following control constructs with examples:

IF

DO

CASE

GOTO

Use Lagrange's formula to compute the value of when x if the following values of x and y are given:

x 1 2 3 4 7
y 2 4 8 16 128

Using Newton-Raphson method, find out the root of the equation correct to three decimal places
x sin x cos x which is near to x =n.

Solve the following system of equations:


4x 3y-z
3x 3z 4

using Gauss-Jordan method with pivoting.

Calculate the value of integral to sin x dx by Simpson's rule using 11 ordinates.

Using Runge-Kutta method of order find y (0·2) for the equation

dy/dx y =l. Take h 0·2.

Find first and second derivative at 1·1 for the data

x 1.00 1.2 1.4 1.6 1.8 2.00
y 0 0.1280 0.5440 1.2960 2.432 4.00

Determine the eigenvalues and corresponding eigenvectors for the matrix A is

6 2
3
2 3

Find inverse of the matrix A is

5 8 1
0 2 1
4 3

and hence solve Ax when b is

1

3

The following table gives the values of x and y. Use appropriate central difference formula to find the value of y when x is 38.
30 35 40 45 50
15·9 14·9 14·1 13·3 12.5

Prove that e^x e^x . E e^x ,interval of differencing being unity.

8. Explain the following:

Lagrange's Mean Value Theorem

Round off and Truncation errors

Numerical Integration

Global and Local Variables