Jawaharlal Nehru Technological University Hyderabad 2011-2nd Year B.E Electrical and Electronics Engineering B.Tech I Semester s, MATHEMATICS-III common to EEE and EC - Question Paper

Code No: A109210201 R09 Set No. 2
II B.Tech I Semester Examinations,MAY 2011
MATHEMATICS-III
Common to ICE, E.COMP.E, ETM, EIE, ECE, EEE
Time: three hours Max Marks: 75
ans any 5 ques.
All ques. carry equal marks
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1. (a) Express x3+3x2+4x+3 interms of Legendre polynomial.
(b) Evaluate
R1
0
x(1 ?? x2)??1
2U4(x)dx. [8+7]
2. obtain the Taylor's and Laurent's series which represents the function (z2??1)
(z+3)(z+2) when
(a) jzj  2
(b) two < jzj < 3
(c) jzj  three [15]
3. (a) obtain the analytic function f(z) = u(r, )+ i v(r, ) such that u(r; ) =
r2 cos 2 ?? r cos  + 2.
(b) S.T. The function u= 1/2 log (x2 + y2) is harmonic & nd its conjugate. [15]
4. (a) Evaluate
1R
0
log x
1+x2 dx
(b) obtain the Residues of f (z) = 1
z(ez??1) [8+7]
5. (a) Evaluate
R
c
(z2 + 3z + 2)dz where C is the arc of the cycloid x=a( + sin), y
= a(1 - cos) ranging from the points (0,0) & (a, 2a)
(b) Evaluate
R
c
(z2 + 3z)dz along the straight line from (2,0) to (2,2) and then
from (2,2) to (0,2) [15]
6. (a) Draw the undirected graph represented by the adjacency matrix A provided beneath.
A =
2
664
1 two 0 0
3 0 one 1
0 one two 2
0 one two 0
3
775
(b) Convert the subsequent tree into binary tree (gure 1). [7+8]
7. Using Jacobi Series, P.T. J2
0 + two fJ2
1 + J2
2 + ????g = one [15]
8. (a) obtain the points at which w = cosh z is not conformal.
(b) obtain the image of the strip bounded by x = 0 and x = 
4 under the transfor-
mation w = cos z [7+8]
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1

Earning:   Approval pending.