Reg. No.
MAT 2102 Page 1 of 2
III SEMESTER B.TECH. (E&C/EE/ICE/BM ENGINEERING)
END SEMESTER EXAMINATIONS, NOV. 2016
SUBJECT: ENGINEERING MATHEMATICS-III [MAT 2102]
REVISED CREDIT SYSTEM
(25/11/2016)
Time: 3 Hours MAX. MARKS: 50
1A.
Find the half range Fourier cosine series expansion of
( ) 1 ,0 .
x
f x x l
l
Also draw the graph of corresponding periodic
extension of f(x).
3
1B.
Find the Fourier transform of
2
3
0
1 , 1 sin cos
( ) .
0, 1
xx t t t
f x and hence evaluate dt
xt
3
1C.
Expand f(x) = xsinx , 0 ≤ x ≤ 2π, f(x+2π) = f(x) as a Fourier series and
hence evaluate
2
2
1
1
nn
.
4
2A.
Find the Fourier cosine transform of
,0
ax
ea
, and hence find
22
Sx
Fax
3
2B.
Find the analytic function f(z) = u+iv for which
sin2
cosh2 cos2
x
uyx
3
2C.
(i) Find all possible expansion of
2
4
() ( 3)( 1)
z
fz zz
about z = -1.
(ii) Expand f(z) = sin2x about z = π/4.
4
3A.
If f(z) = u + iv is analytic function of z , show that
22 2
p p 2
22
u p p 1 u f (z)
xy
3
Instructions to Candidates:
Answer ALL the questions.
