Mathematics II 2008
Mathematics II 2008
Mathematics II 2008
2015.'r
Second Semester
.\
Civit Engineering
MA 2161/1VIA 22IO8OO3OOO4
(Common to all
MATHEMATICS _ II
Branches)
(Regulatiqns 2008)
= sin(2logr)
equation with constant coefficient
I.
2.
ff-;
"ort;ff*
e-t
that
rr.
(-
^^^fC^:^-{
-!^-!
lf"an
yax.
,l x&y --^vd.x.
- zb
'closedcurve Ci"
-
5.
invariant points of w =
*,
7.
Evaluate [ :u-"",;;arwhere
C is the circle l, t"z(z _L)
8.
9.
Defi.ne es.sential
10.
Evaluate
gl
Iy{*by
-0
using taplace
Transform.
.r
,.r4.
\
,.i. .
PART B
(5 x 16 = 80 marks).
(i)
\-/ Solve:
-- dX +18y = e*2* +e-" cosr + tr .
------ tI
dX,-n9
1,1. (a)
(u)
**,'#
+2x -2,
r,ff-*x
+2g o
(8)
uo
(8)
,,
(i)
@)
Solve
d,2,t
-:
(8)
.
.t
.':.,0f
',
(s)'
dx'
-:--
x' + !'
= a2 ,2 =.0 and
z --.h.
(10)
..:
(b) ''r,
(i)'
o.?
,?
--i
(\xz - z>j + (3w' - yY
is a eonse{vative
'=
of
(6)
F'.
oounded by the
13. (a) (D
(ii)
t(x.#)
"
faee
in a regibn R, prove
(8)
analvtic
poi-nts
Or
(b) (r) If
,'::
f (z)
=u+iu
sinZ*
is
.: : r'
U*U=-:f:---.
cosh2y-- cosZx
,
(ii)
the region
Under the transformation w=ldetermine
7
in ru-plane
;< i <;.
(8)
2171L
formula.
(u)
'.ru'&
Uvaluate
(8)
.. 1
2sl----t.
x* +a-
'
..
..
.(
ir:.
(8)
:.
Or
..i
.L/
(ii)
. Ry- usin
Cau
where C is lzl=
15.
'
+ @srz
l---------dz
L@ + 2){z +l)'
t sinte
S.
(a)
(b) , '(i)
',' ., ,, (ii)
'
:.:i-
217!/.L