Aligarh Muslim University (AMU) 2009 B.Sc Mathematics -(Numerical Analysis) - Question Paper
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2008-2009
3.A. / B.Sc. (HONS.) (PART-I) EXAMINATION (MATHEMATICS)
NUMERICAL ANALYSIS (MM-106)
Find a root correct to three decimal places of the equation x cosx = 0 by Newton (4,4) Raphson method.
find the rmverse of the matrix.
OR
(b ) Solve the following system of equations by factorization method :
..... _ ___ 2x-*7 3y + z = 9
x + 2y + 3z = 6 3x + y + 2z = 8
2. (a) Using Gausss backward difference interpolation formula, find the value of f(32), given (4,4) that f(25) = 0.2707, f(30) = 0.3027, f(35) = 0.3386 ; f(40) = 0.3794
OR
(a7) Use Stirlings formula to find U32 from the following data:
U20 = -14.035; U25= 13.674; u = 13.257
u35 = 12.734 ;u4o= 1Z089 ; 1145= 11-309
t *
(b) Find the Lagrange interpolating polynomial of degree 2 approximating the function y = In x defined by following table of values and hence determine the value of In 2.7
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2.5 |
3.0 |
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y = In x |
0.69315 |
0.91629 |
1.09861 |
3. (a) Derive Simpsons 3/8 rule
(4,4)
* 3
o
1 J I
and use it to evaluate |-dx with h = .
} + x 6
OR
Contd.....2
a) Derive Weddles rule
r
Jy<ty = , - O'o + 5 + >2 + 6y} + y* + 5ys + y6)
10
-u,
71
-dx
and use it to obtain an approximate value of n from the formula
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(b) A curve is given by the points of the table given below: | ||||||||||||||||||||
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Calculate the area bounded by the curve, the x-axis and the extreme ordinates.
(a) Determine the value of y at x = 0.1 given that y (0) = 1 and y ~ xJ + y by Eulers (4,4) method
(b) Given the differential equation
dy _ x1 dx y*+l
with initial condition y = 0 when x = 0, obtain-y for x = 0.25 ; 0-5 and 1.0 by Picards method.
OR
(b*) Given ;
dy_
dx
= l+y ; y (0) = 0,
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Find y (0.2) ; y (0.4) and y (0.6) using second order Runge-Kutta method. 5; (a} Fit a curve y abx to the following data: | ||||||||||||
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(b) Solve any TWO of the following equations:
(4,4
(i) ux+2 - 4ux = 9xJ
(ii) ux+2 - 3ux+i - 4ux = 3X
(iii) ux+2 - 2ux+1 + th- = 3x + 4
(iv) nx+2 7ux+i + 12ux = cos x with uo 0 = ui.
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Attachment: |
| Earning: Approval pending. |
