Osmania University (OU) 2007 B.E Computer Science Mathematics-3 - Question Paper
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Code No. 4009/N FACULTY OF ENGINEERING
B.E. 2/4 I~Sem (New) (Common to all Branches Except- IT)
Suppl. Examination May/June - 2008 Subject: Mathematics-Ill
Time: 3 hours ] [Max. Marks: 75 Note : Answer all questions of Part A,
Answer five questions from Fart B
1. Eliminating the arbitrary constants a aid b from z = ax + by + a2b2, obtain the
Find the complete integral of the partial differential equation
p*qJ(px + qy - z) = 2 2
to 3. Find the Fourier Series expansion of ./(x) = x, -n < x < n,
fa+2%) =/x). 3
r
4. Fourier cosine series of/(x) - 1, 0 < x < 2, is...............................: 2
5. Give dimensional wave equation is_____2
6. Explain the method of separation of variables. 3
7. , Contain the z transform ofy = Cos h(n0) 2
z
8. Find the inverse z-transform of F(z) = (z- 2) 3
9. Derive Newtons forward Interpolation formula 3
r* dx 1
10. Evaluate : JQ y2 by Simpsons j formula with n = 10. 3
PART - B (5* 10=50 marks)
11. (a) Solve : z(z2 + xy) (px - qy) = x4 5 (b) Solve :zpq = p + q 5
12. (a) Find Fourier Series of/(x) = x3 in (-tt, te) 5 (b) Find the Fourier Sine and Cosine series of
13. Find the temperature in a thin metal rod of length L, with both the ends insulated and with initial temperature Sini-|! in the rod. 10
14. (a) Find the z transform of Cos(n + 1)0. 5 (b) State and prove convolution theorem of z-transform. 5
15. (a) Use Lagranges interpolation formula to fit a polynomial to the following
data. Hence find y(-2), y(l) and y(4). x: -1 0 2 3
(b) Using fourth order Runge-Kutta method find the solution of
dy
-j = y-x, with initial condition y(0) = 1.5 on[0,1] 5
16. Solve (ex ~ 1) (qr - ps) = pqex, by using Monges method. 10
17. Solve the following system of equations by Gauss elimination method.
4x ~ 3y - 9z + 6w = 0
2x + 3y + 3z + 6w = 6
4x - 21y - 39z - 6w = -24. 10
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