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Code: 15A54201
B.Tech I Year II Semester (R15) Supplementary Examinations November 2017
MATHEMATICS ? II
(Common to all)
Time: 3 hours Max. Marks: 70
PART ? A
(Compulsory Question)
*****
1 Answer the following: (10 X 02 = 20 Marks)
(a)
Find inverse transform of
) 4 (
1
+ s s
(b) Define unit impulse function of Laplace transform.
(c) If x
4
in (-1, 1) then find the Fourier coefficient of
(d) Obtain the Fourier series for the function = x in the interval
(e)
Find the Fourier cosine transform of .
(f) Find the Fourier sine transform of
x
e
?
.
(g) Solve p
2
-q
2
= x-y.
(h) Solve q
2
= z
2
p
2
(1 - p
2
).
(i) Find
(j) Find Z transform of n
3
.
PART ? B
(Answer all five units, 5 X 10 = 50 Marks)
UNIT ? I
2 (a)
Apply Convolution theorem , Evaluate
?
?
?
?
?
?
?
?
+ +
?
) )( (
1
1
b s a s
L
(b) Solve 0 ) 0 ( , 2 ) ( , 0
2
2
= ? = = + + y o y xy
dx
dy
dx
y d
x using Laplace transform method.
OR
3
Define Periodic function. Evaluate
?
?
?
?
?
?
?
?
?
? t t
dt
t
t e
t L
0
sin
UNIT ? II
4 Expand as a Fourier series in the interval (0, 2 ? ).
OR
5
Obtain a half range sine series for the function: =
?
?
?
?
?
?
?
? ? ?
? ? ?
1
2
1
,
4
3
2
1
0 ,
4
1
x x
x x
Contd. in page 2
Page 1 of 2
R15
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Code: 15A54201
B.Tech I Year II Semester (R15) Supplementary Examinations November 2017
MATHEMATICS ? II
(Common to all)
Time: 3 hours Max. Marks: 70
PART ? A
(Compulsory Question)
*****
1 Answer the following: (10 X 02 = 20 Marks)
(a)
Find inverse transform of
) 4 (
1
+ s s
(b) Define unit impulse function of Laplace transform.
(c) If x
4
in (-1, 1) then find the Fourier coefficient of
(d) Obtain the Fourier series for the function = x in the interval
(e)
Find the Fourier cosine transform of .
(f) Find the Fourier sine transform of
x
e
?
.
(g) Solve p
2
-q
2
= x-y.
(h) Solve q
2
= z
2
p
2
(1 - p
2
).
(i) Find
(j) Find Z transform of n
3
.
PART ? B
(Answer all five units, 5 X 10 = 50 Marks)
UNIT ? I
2 (a)
Apply Convolution theorem , Evaluate
?
?
?
?
?
?
?
?
+ +
?
) )( (
1
1
b s a s
L
(b) Solve 0 ) 0 ( , 2 ) ( , 0
2
2
= ? = = + + y o y xy
dx
dy
dx
y d
x using Laplace transform method.
OR
3
Define Periodic function. Evaluate
?
?
?
?
?
?
?
?
?
? t t
dt
t
t e
t L
0
sin
UNIT ? II
4 Expand as a Fourier series in the interval (0, 2 ? ).
OR
5
Obtain a half range sine series for the function: =
?
?
?
?
?
?
?
? ? ?
? ? ?
1
2
1
,
4
3
2
1
0 ,
4
1
x x
x x
Contd. in page 2
Page 1 of 2
R15
Code: 15A54201
UNIT ? III
6
(a)
Find the Fourier transform of
?
?
?
?
?
>
? ?
1 , 0
1 , 1
2
x
x x
Hence evaluate
dx
x
x
x x x
?
?
?
?
?
? ?
?
?
2
cos
sin cos
0
3
(b) Write the conditions of Parseval?s identity for Fourier transforms.
OR
7
Find the Fourier sine transform of
( )
2 2
1
a x x +
UNIT ? IV
8 (a)
Form the partial differential equation ( ) ( ) x y f x y f z 3 2
2 1
? + + =
by eliminating the arbitrary function.
(b) Use the method of separation of variables, solve u
t
u
x
u
+
?
?
=
?
?
2 where u(x, 0) = 6e
-3x
.
OR
9
Solve the Laplace equation 0
2
2
2
2
=
?
?
+
?
?
y
u
x
u
subject to the conditions and
?
?
?
?
?
?
l
x n ?
UNIT ? V
10 (a) Find the Z-transformation of .
(b) If U(z)=
4
2
) 1 (
12 3 2
?
+ +
z
z z
, evaluate
3 2
,U U using Initial Value Theorem.
OR
11
Solve the differential equation 5 3 2
1 2
+ = + ?
+ +
n u u u
n n n
using Z-transforms.
*****
Page 2 of 2
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This post was last modified on 11 September 2020