## March 9, 2010

### ENGINEERING MATHEMATICS 111 QUESTION PAPER

ANNA UNIVERSITY COIMBATORE
B.E/B.TECH.DEGREE EXAMINATIONS:SEPTEMBER 2009
REGULATIONS-2007 THIRD SEMESTER

ENGINEERING MATHEMATICS 111
(COMMON TO CIVIL/AERONAUTICAL/CSE/IT)
TIME:3 Hours Max.Marks:100
PART-A
1.Form partial differential equation by eliminating the arbitary constants from z=ax+by+a
2.solve p+q=4.
3.solve(D-6DD'+9d')z=0
4.findthe P.I of(D-4DD')z=e
5.state the dirichlet's conditions for the existence of Fourier series for f(x).
6.write the formulae for Fourier constants for f(x)in the interval (-1,2).
7.obtain the sine series fo the unity in (0,3).
8.if f(x)=|x| expanded as a Foutrier series in 0<4,find a.
9.Explain the method of separation of variables.
10.state the assumptions made in the derivation of one dimentional wave equation.
11.state one dimentional heat equation with the initial boundary conditions.
12.when the ends of the road 20 cm are maintained at the temperature 283k and 293k respectively until steady state prevailed.determine the steady state temperature of the rod.
13.state the Fourier integral theorem
14.find the sine transform of e power -x.
15.state shifting theorem on fourier transform.
16.state convolution theorem for fourier transform.
17.prove that z(a power n)=z/z-a
18.find Z(sinat)
19.find Z power -1[z power 2/(z-a) power 2.
20.state the final value theorem on Z transforms

PART-B (5x12=60 marks)
21.a)form partial differential equation dy eliminating the arbitary functions f and g in z=x square f(y)+y square g(x)
b)find the singular integral of z=px+qy+2 root of pq.
22.a)solve p square + q square =x square + y square.
b)solve(D cube-4D square D'+ 4DD')z=6 sin(3x+6y)
23.find the fourier series of f(x)=x in (0,pie)
24.a)obtain the half range cosine series for f(x)=cosax in -pie
25.A string is stretched and fastened to two points l apart.Motion is started displacing the string into the form of the curve y=k(lx=x square) and then released from rest in this position.find the displacement y(x,t).
26.find the steady state temperature distribution in a square plate bounded by the lines x=0,y=0,x=20,y=20,.it's surfaces are in sulated satisfying the boundary conditions U(0,y)=U(20,y)=U(x,20)=x(20-x).
27.a)find the fourier transform of f(x)={x,|x|
0,|x|>a}
b)evaluate integral 0 to infinity dx/(x square + a square )(x square + b square) using transforms
28.solve the difference equation using Z transform method:
y base n+2-3 base n+1 + 2y base n=n2 power n givwn that y(0)=0,y(1)=0.

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