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CLASS: B.Stat.
St. JOSEPH’S COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI – 620 002
SEMESTER EXAMINATIONS – APRIL 2015
TIME: 3 Hrs.
MAXIMUM MARKS: 100
SEM
SET
PAPER CODE
TITLE OF THE PAPER
IV
2013
11UST430301A
NUMERICAL MATHEMATICS
SECTION – A
Answer all the questions:
Choose the correct answer:
20 x 1 = 20
1. The backward difference operator is defined by
b) —y n = y n -1 - y n
a) —y n = y n - y n -1
c) —y n = y n - y n +1
d) —y n = y n - y0
2. Bessel’s formula is obtained from some modifications of
a) Newton’s forward
b) Gauss’s forward
c) Newton’s backward
d) Gauss’s backward
3. Successive approximation’s method starts with
a) Newton’s forward difference formula
b) Newton’s divided difference formula
c) Newton’s backward difference formula
d) Lagrange’s interpolation formula
4. Regula falsi method is also known as
a) Method of Newton Raphson b) Method of chords
c) Method of false position
d) b and c
5. In general quadrature formula if we put n = 2 we get
b) Weddle’s rule
a) Simpson’s 1 rule
3
th
d) None of these
Simpson’s 3 8 rule
Fill in the blanks:
6. The process of computing the value of a function inside the given
range is called ______.
c)
7.
The mean of Gauss forward and Gauss backward formula is
_______.
8.
Lagrange’s interpolation formula is ______ .
9.
If f(a) is –ve and f(b) is +ve, then a root lies between ______ and
______.
10.
th
Simpson’s 3 8 rule is ______.
State True or False:
11. E = 1 + D.
12. Laplase-Everett’s formula is derived from Gauss’s backward
interpolation formula.
13. Inverse interpolation is in general, finding the value of x for a
given value of f(x).
14. Newton’s Raphson method is also referred to as the method of
tangent.
15. Simpson’s 3/8 rule can be applied only if the number of sub
intervals is a multiple of 4.
Match the following:
16. D log f(x)
- a) d
17. Central difference operator - b) n = 2
18. Elimination of third order
differences
19. x n +1
20. Simpson’s 1/3 rule
È Df ( x ) ˘
log
c)
Í1 + f ( x ) ˙
Î
˚
- d) Inverse interpolation
-
f (x n )
e) x n f ¢( x n )
SECTION – B
Answer all the questions:
21. a. Derive Newton divided difference formula.
5 x 4 = 20
OR
b. Using the following table find f(656)
x:
654
658
659
661
y : 2.8156 2.8182 2.8189 2.8202
22. a. Derive Stirling’s formula for interpolation.
OR
b. Using Bessel’s formula find f(25) given f(20) = 2854,
f(24) = 3162, f(28) = 3544, f(32) = 3992.
23. a. Explain the method of successive approximation.
OR
b. Tabulate y = x3 for x = 2, 3, 4, 5 and calculate the cube root of
10 correct to three decimal places.
24. a. Find the smallest positive root of the equation x3 – 2x + 0.5 = 0
using Newton’s Raphson method.
OR
b. Find the approximate value of real root of xlog10x = 1.2 by
regular falsi method.
25. a.
d2y
From the following table, obtain
at the point x = 0.96.
2
dx
x : 0.96
0.98
1.00
1.02
1.04
f ( x : 0.7825 0.7739 0.7651 0.7563 0.7473
OR
1 dx
b.
using Trapezoidal rule with h = 0.2.
Evaluate Ú
2
01 + x
SECTION – C
Answer any FOUR questions:
4 x 15 = 60
26. a) Derive Newton-Gregory formula for forward interpolation.
b) The following table gives certain corresponding values of x
and log10x. Compute the value of log10323.5, by using
Lagrange’s interpolation formula.
x
: 321 .0
322 .8
324 .2
325 .0
log10 x : 2.50651 2.50893 2.51081 2.51188
27. a) Using Stirling’s formula to evaluate f(1.22) given:
x : 1.0
1.1
1.2
1.3
1.4
f ( x ) : 0.841 0.891 0.932 0.963 0.985
b) Drive Everett’s formula.
28. Find the value of x when y =85 using Lagrange’s formula for
inverse interpolation from the following table.
x: 2
5
8
14
y : 94 .8 87 .9 81 .3 68 .7
29. Find a real root of the equation x3 – 2x – 5 = 0, using the Bisection
method.
30. Derive Weddle’s formula for numerical integration.
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