Numerical Analysis 2017 – BSc Computer Science Part 2 (MJPRU)
Paper code: 13512
1512
B.Sc. (Computer Science) (Part 2)
Examination, 2017
Paper No. 1.3
NUMERICAL ANALYSIS
Time: Three Hours] [Maximum Marks: 50
Note: Attempt five questions. All questions carry equal marks.
1. (a) Use Lagrange’s formula to find f(6) from the following table:
2
5
7
10
12
18
180
448
1210
2028
(b) The population (in thousands) of a town in the year 1931, …………, 1971 are as ahead:
1931
1941
1951
1961
1971
15
20
27
39
52
Find the population of the town in 1946 by applying Gauss’s backward formula.
2. (a) Use the Milne’s method to solve the equation 
with y(0)=0 from x=0 to x=1.
(b) Use the Runge-Kutta method to approximate y when x=0.1 given that x=0 when y=2 and \frac{dy}{dx}=y-x.
3. (a) Find a real root of the equation 
using the Newton-Raphson method.
(b) Find the cube root of 10 correct to three decimal places by Regula-Falsi method.
4. (a) Evaluate 
by Simpson’s one-third rule by dividing the interval into 6 parts.
(b) Evaluate 
by Trapezoidal rule.
5. (a) Solve the following equations by Gauss Elimination method:
(b) Solve by Jacobi iteration method the system of equations:
6. (a) State and prove Newton’s-Gregory formula for backward interpolation.
(b) Apply Newton’s dividend difference formula to find the value of f(8) if f91)=3, f(3)=31, f(6)=223, f(10)=1011, f(11)=1343.
7. (a) Find the function 
in powers of x-1 given that
, 
, 
, 
.
(b) Write short notes on the following:
- Relative Error and Absolute Error
- Percentage Error and Round Off Error
8. (a) Solve the system linear of equations by the Gauss-Seidel method (4 iterations):
(b) Solve the following:
(i) Prove that:
(ii) Prove that:
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