# Transforms and partial Differential Equations ND12 MA2211

Question Paper Code : 11485
B. E. /B. Tech. DE GREE EXAMINATION, NOVEMBER/DECEMBER 2012.
Third Semester -Civil Engineering
MA 2211/MA 3144/CK 201110L77 MA 301/080100008/080210001/
MAU 211/ETMA 927I - TRANSFORMS AND PARTIAL DIFFERENTIAL
EQUATIONS
(Common to all branches)
(Regulation 2008)

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PARTA-(10 x2=2Omarks)

1. Find the co-efficient b, of the Fourier series for the function f (x) = r sin r in (-2,2).
2. Define Root Mean Square value of a function /(r) over the interval (a, b).
3. Find. the Fourier transform of e-"|*l , o, O .
4. State convolution theorem in Fourier transform.
5. Eliminate the arbitrary function 'f from ' " = f'\(*Z)) and form the PDE.
6. Soive : (D - 1)(D- D +l)z =A.
7. An insulated rod of length 60 cm has its ends at A and B maintained at 20'C and 80oC respectively. Find the steady state solution ofthe rod.
8. Aplateisboundedbythelines *=0, !=0, x=l and y=l.Its facesare insulated. The edge coinciding with r-axis is kept at 100"C. The edge coinciding with y-axis is kept at 50oC. The other two edges are kept at 0'C. Write the boundary conditions that are needed for solving two dimensional heat flow equation.
9. Find the Z-transform of a" .
10. Solve Jn+r*2yn =0, given that y(0) =2.

PARTB-(5x16=80marks)

11. (a) (, Find the Fourier series expansion of f (x) = x * x2 in (-r, n) . (8)
(ii) Find the Fourier series expansion of .:1x1={x^' 0 < r < 1 . anso
Or
(b) (i) Obtain the half range cosine series for f (x) = x in (0, o). (8)
(ii) Find the Fourier series as far as the second harmonic to represent the function /(r) with period 6, given in the following table : (8)