CLASS: B.STAT
11A/361
St. JOSEPH’S COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI – 620 002
SEMESTER EXAMINATIONS - APRIL 2011
TIME: 3 Hrs.
MAXIMUM MARKS: 100
SEM
SET
PAPER CODE
TITLE OF THE PAPER
IV
2009
08UST430301A
CORE ELECTIVE : NUMERICAL MATHEMATICS
SECTION – A
Answer all the questions:
Choose the correct answer:
1.
2.
3.
4.
5.
20 x 1 = 20
The nth ________ differences of a polynomial of nth degree are constant.
a)
Divided difference
b)
Forward difference
c)
Backward difference
d)
All the above
Stirling’s formula is the average of two
a)
Gauss formula
b)
Newton’s formula
c)
Simpson’s formula
d)
Regula falsi formula
_________ interpolation is defind as the process of calculating the value of the argument,
corresponding to a given functional value.
a)
Bessel’s
b)
Inverse
c)
Divided
d)
Stirling’s
The criterion for the convergence of Newton’s Raphson method is
a)
f ( x ) f ( x )  f ( x )
b)
f ( x )  f ( x )
c)
f ( x )  f ( x )
d)
f ( x ) f ( x )  [f ( x )]2
The degree of a polynomial y(x), in simpson’s one-third rule
a)
One
c) Three
Fill in the blanks:
b)
Two
d)
four
6.
Newton forward interpolation formula is _________.
7.
Gauss forward formula involves ________ differences below the central line.
8.
Successive approximation method is used in ________ interpolation.
9.
Regula falsi method is also known as, the method of ________ position.
10.
In weddle’s rule, y(x) is a polynomial of degree ______.
State True or False:
11.
The value of any divided difference is independent of the order of the arguments.
12.
Gauss backward formula is useful when u lies between -1 and 0.
13.
The sequence {x0, x1, x2….xn} is called the sequence of successive approximation.
14.
If f(a) and f(b) have opposite signs then one root of f(x)=0 lies between a and b.
15. In simpson’s three-eighth rule, y(x) is a polynomial of degree three.
Answer in one or two sentences:
16.
Write the Newton’s forward interpolation formula.
17.
Write down Bessel’s formula for interpolation.
18.
State lagrange’s interpolation formula.
19.
Explain the bisection method.
20.
Write simpson’s one-third rule.
SECTION – B
Answer all the questions:
21.
a.
5 x 4 = 20
Derive Newton’s forward interpolation formula.
OR
From the following table, find f(x) using Newton’s divided difference formula.
x :
1
2
7
8
f(x) :
1
5
5
4
a.
From the following table,
x
:
20
25
30
35
40
f(x) :
11.4699
12.7834
13.7648
14.4982
15.0463
Find f(34) using Everett’s formula.
b.
22.
OR
b.
Apply gauss forward formula to obtain f(x) at x=3.5 from the table below.
x
:
f (x) :
2
3
4
5
2.626
3.454
4.784
6.986
23.
a.
Explain the method of successive approximation.
OR
24.
b.
Apply Lagrange’s formula inversely to find correct to two decimal places, the value of
x when y=f(x)=19, given the following table.
x
:
0
1
2
Y=f(x) :
0
1
20
a.
Find the positive root of x3-x=1 correct to four decimal places by bisection method.
OR
25.
b.
Find an approximate root of x3-4x+1=0 by Regula falsi method.
a.
Derive simpson’s one-third rule from the general quadrature formula.
OR
b.
x
:
f(x) :
The following values of yx are given.
0
1
2
0.146
0.161
0.176
3
0.190
4
0.204
5
0.217
6
0.230
6
Using Trapezoidal rule find the value of
 y x dx
0
SECTION – C
Answer any FOUR questions:
4 x 15 = 60
26.
Using Lagrange’s interpolation formula, find y(10) from the following table.
x :
5
6
9
11
y :
12
13
14
16
27.
Given the following table, find y(35) by using Bessel’s formula.
x :
20
30
40
50
y :
512
439
346
243
28.
The following values of y=f(x) are given
x :
10
15
20
f(x) :
1754
2648
3564
Find the value of x for f(x)=3000 by successive approximation method.
Find the positive root of f(x) = 2x3-3x-6=0 by Newton Raphson method correct to five decimal
places.
29.
30.
Evaluate I=
6 1

01  x
dx using weddle’s rule.
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