Paper code: 13512
B.Sc. (Computer Science) (Part 2)
Paper No. 1.3
Time: Three Hours] [Maximum Marks: 50
Note: Attempt five questions. All questions carry equal marks. Symbols are as usual use or calculator is allowed.
1. (a) Show that:
(b) Estimate the missing term in the following table:
Explain why value differs from or 27?
2. (a) Given:
(b) Use the method of separation of symbols to prove that:
3. (a) State and prove Newton-Gregory formula for forward interpolation.
(b) , find the divided differences:
f(a,b), f(a,b,c) And f(a,b,c,d) ?
- (a) Find by using Simpson’s 1/3 and 3/8 Hence obtain the approximate value of in each case.
(b) Find first and second derivatives of the function given below at the point x=1.2:
5. (a) Show that the expirations given below are approximations to the third derivative of .
(b) Define the following:
- Inherent errors
- Round-off errors
- Truncation errors
6. (a) Solve the following system of equations by Gaussian elimination method:
(b) Find the solutions of the system:
7. Tabulate by Milne’s method the numerical solution of with , from x=0.20 to x=0.30.
8. (a) Find the real root of the equation correct to four places of decimals by Newton-Rap son method.
(b) Show that the square root of N=AB is given by where .
9. (a) Determine the real root of by iteration method.
(b) Use Runge-Kutta Method to approximate y, when x=0.1 and x=0.2 and , given that x=0, y=1 and .