Calicut University 2006 B.Tech Electronics and Communications Engineering maths 4 - Question Paper
Reg. No...........-..................
FOURTH SEMESTER B.TECIL (ENGINEERING) DEGREE EXAMINATION, JUNE 2000
EN 04. 401 (A)ENGINEERING MATHEMATICSrV
{Common to aJI branches except CS mid IT)
Thrttffours Maximum : 100 Marks Anatotr all qutntionn,
(n) Ihow that f(z)m{x/ry\ j, discontinuous at the origin, riven that/70) a 0.
x + y*
ft) Writ* the C.R. equations in polar co-ordinate*. fc) OhUfn the expansion of log (1 + t) when \m | < 1 using Taylor aeries.
M) fmd zeros and injfuJariUe* of the function fir)- 1
#j ft ova Umt J win x.
if) fxprws x3 2x3 - x - 3 in term* of Legendre polynomials.
dz 3 2 a
(g) Solve by method of Reparation of variables y + "
(b) Vrite down the poaaible solutions of wnve equation (in one-dimensional).
VD/ (8 x 6 * 40 marks)
Uifi* ! there any analytic function fix) u + io for which v * ey V
(7 marks)
ft Discuss the transformation w~r.
(Wf) Show that the map w * - maps the totality ofcircles and linee as circlc or lines.
(8 marks)
|i) Find tha bilinear transformation that mapa 1, i and - 1 of the r-plane onto 0,1 and of J>f w-plan*.
(7 marks)
2
U-
/.I
*
3. (*) (i) Evaluate using Cauchy's integral formultt /-5--d2* where C is the cj
\t + I + j | - 2.
(ii) Evaluate j
13+ 5 fin 0
dQ
1
(8 i
(7nv
Or
1
r
I
2
(b) (i) Find the polae and residues of/<!)--1- at each point.
<8 j
1.
1
(ii) Obtain the Laurent* expansion of f(z)
in J < |*| < 2.
(7
(x-!)<*-2)
4. (a) Using RodriguVs formula for ?n (x), prove that J Pm (x) Vn (x)dx
I
0
whonm* 2
-i
when
m
(15 3.
I
(15 mi m
2m +1
Or
(b) Derive the recurrence formulae nVix)mx J*(x)-F |U)
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Attachment: |
| Earning: Approval pending. |
