Aligarh Muslim University (AMU) 2010 B.Sc Mathematics -(Numerical Analysis) - Question Paper
(4243)
2009-2010
B.A./B.Sc. (Hods.) (PART -1) EXAMINATION (MATHEMATICS)
NUMERICAL ANALYSIS (MM -106)
Maximum Marks: 40
Duration: Three Hours
Note: Answer all questions.
1- (a) f5 -2 1 1 ' * - CM)
Decompos
e the matrix A =
7 1 -5 3 7 4
into the LU form with t =1, i = 1,2,3 and solve the system AX=b where b=[4 8 lOj*. Determine L1 and IT1 and hence find A'1
(b) Using Newton-Raphson method obtain a root correct to three decimal places of the equation x-cosx = 0
OR
"(o') eteimirio- the largest eigen value and the corresponding eigen
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vector of the matrix A - |
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2 (a) Values of x (in degrees ) and Sin x are given in the following table (4,4)
|
X |
Sin x |
|
15 |
0.2588190 |
|
20 |
03420201 |
|
25 |
0.4226183 |
|
30 |
0-5 |
|
35 |
0.5735764 |
Find the values of
0) Sin 16 and Sin 32 using Newton Gregory formulae
(ii) Sing 26 using first three terms of Stirlings formula OR
(a') Using the following data
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Find x at y = 45 and 825 by inverse interpolation formula. |
Contd.....2
(b) Show that
(i) E"' = I-V
(ii)
(iii) AVyk =Ayk =5Jy*
(a) A r- (4,4)
Evaluate |* VSinG d0
(i) UsingSimpson's rule three times
8
(ii) Using Weddles rule once ~~
OR
(a') The following table of values of x and y is given by
|
x |
y |
|
1 |
7.4036 |
|
2 |
7.7815 |
|
3 |
8.1291 |
|
4 |
8.4510 |
dy
Find (i) ~r~ when x =1, x = 4.5 ax *-
(ii) From this table, find x, correct to two decimal places for
which y is maximum '
(b) 3
Derive Simpsons - rul
r,ydx = h(y, + 3y,+3yI+y3)
Using this rule, evaluate
I = (*dx with h = .
*l + x 6
(a) dy -j (4,4)
Given = 1 + y , where y = 0 when x =0, the Runge-Kutta,
method of fourth order produces the following values of y at x = 0.2,
0.4 and 0.6
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Use this data and compute the value of y at x Moulton method. OR 0.8 using Adams- |
7
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Attachment: |
| Earning: Approval pending. |
