BACHELOR IN COMPUTER APPLICATIONS Term-End Examination June, 2OO7 GS-71: GOIUPUTER ORTENTED NUMERICAL TECHNIOUES Time : 3 hours
Maximum Marks : 75
Note r
Qu estion number 1 is compulsory. Attempt any three questionsfrom the rest. In total you haue to enswer four questions.
(a)
If the number x* : 4.8 approximatesthe number x : 4'305 correct upto n significantdecimal digits, then calculatethe value of n .
l.
(b)
Let f(x) : xl/La , and supposethat x approximatesx* correct upto L2 significant digits. Then compute upto how many significant decimal digits f(x-) approximatesf(x).
(c)
Give one example of an equation with "multiple roots". And justify your answer. Also, write a polynomial equation of degree three which has a
s
double root 62 and a single root 0.
CS-71
P.T.O.
(d)
Estimate the missing data entry (a) using Newton's divided differencemethd :
(e)
x
1
2
a
4
f(x)
3
0
2
4
If f(x) : x3, then Prove that for a c f[a, b, cl
(0
2.
(a)
Prove that hD = log" E, where D stands f or and E is the advanceoperator.
3'[d " d"
5
Find a real root correct upto three decimal places of the function 0H:*3
2x
using (i)
Bisection method,
(ii)
Newton Raphsonmethod.
5+5:70
the (b) 5 :',trffiffiil:lfi'ffi';il"1"'obtain
CS-71
x
0
1
3
4
v(x)
2
0
1
2
(a)
3.
Solve the system of following equations using Gauss Elimination method |
5
3xr+2xr+*3=3 2x1+x2+x3=0 6xr+2xr+4xr=6 (b)
(c)
When is a matrix A said to be strictly diagonally dominant ? Gir.re an. example of 3 x 3 matrix A which is strictly diagonally dominant.
5
Find the minimum number of intervals required to evaluate 1
I d x
J0 l + x
'
4.
(a)
- ]3 -1". with an accuracyof 10-5 using Simpsor,',
5
Find a solution of the system of linear equations z
5
83x+l1y-42=95 7x+52y+l3z=104 3x+8y+292=7L (b)
Given 13 = 1,23 = 8 and 43 = 64. Using numerical differentiation, compute the value of 32 from these' 5
data. 1
(c)
Evaluate t 4
i I+x"
with
six subintervals using
Trapezoidal ,rtile. Hence find an approximate value of fi.
CS-71
P.T.O.
5.
(a)
In RKM of second order or third order or fourth order, what is the significanceof the term "order" ? Explain it for all the above cases by taking one example of each order.
( b ) S o l v e t h e l V tPy ' : y + x , V ( 0 ) : l w i t h h : 0 . 1 the intervalt0, 0.21 using Euler'smethod.
in
' '! (c) If u:4*2Y3 and errors in x, g, z be 0'001, T compute the relativemaximum error in u when x : y : z: 1.
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