Download PTU M.Tech. ECE 1st Semester 36202 ADVANCED MATHEMATICS FOR ENGINEERS Question Paper

Download PTU. I.K. Gujral Punjab Technical University (IKGPTU) M.Tech. ECE 1st Semester 36202 ADVANCED MATHEMATICS FOR ENGINEERS Question Paper.

1 | M-36202 (S9)-500

ARoll No. Total No. of Pages : 02
Total No. of Questions : 08
M.Tech. (ECE) (Sem.?1)
ADVANCED MATHEMATICS FOR ENGINEERS
Subject Code : EC-501
M.Code : 36202
Time : 3 Hrs. Max. Marks : 100

INSTRUCTION TO CANDIDATES :
1. Attempt any FIVE questions out of EIGHT questions.
2. Each question carries TWENTY marks.

Q1. a) Find the fourier sine and cosine transforms of f (x) = e
?ax
(a > 0). (10)
b) If F (f (x)) = F (s) then show that ( ( )) ( ) ( )
n
n n
n
d
F x f x i F s
dx
? ? . (10)
Q2. a) Find the Z-transform of sin
2
k ? ? ?
? ?
? ?
? ?
. (10)
b) If Z (f (k)) = F(z) then show that
1
( )
( ))
1
k
n
F z
Z f n
z
? ? ? ?
? ?
?
? ?
?
? ?
?
(10)
Q3. Apply Gauss-Seidel?s iteration method to solve the equations
20x + y ? 2z = 17; 3x + 20y ? z = ?18; 2x ? 3y + 20z = 25 (20)
Q4. Show that the transformation
1
1
z
w i
z
?
?
?
transform the circle | z | = 1 onto the real axis of
the w ? plane and the interior of the circle into the upper half of the w ? plane. (20)
Q5. Define Euler?s equation and find the shape of the curve of the given perimeter enclosing
maximum area. (20)
Q6. Discuss Hamilton?s principle and drive Lagrange?s equation. (20)


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1 | M-36202 (S9)-500

ARoll No. Total No. of Pages : 02
Total No. of Questions : 08
M.Tech. (ECE) (Sem.?1)
ADVANCED MATHEMATICS FOR ENGINEERS
Subject Code : EC-501
M.Code : 36202
Time : 3 Hrs. Max. Marks : 100

INSTRUCTION TO CANDIDATES :
1. Attempt any FIVE questions out of EIGHT questions.
2. Each question carries TWENTY marks.

Q1. a) Find the fourier sine and cosine transforms of f (x) = e
?ax
(a > 0). (10)
b) If F (f (x)) = F (s) then show that ( ( )) ( ) ( )
n
n n
n
d
F x f x i F s
dx
? ? . (10)
Q2. a) Find the Z-transform of sin
2
k ? ? ?
? ?
? ?
? ?
. (10)
b) If Z (f (k)) = F(z) then show that
1
( )
( ))
1
k
n
F z
Z f n
z
? ? ? ?
? ?
?
? ?
?
? ?
?
(10)
Q3. Apply Gauss-Seidel?s iteration method to solve the equations
20x + y ? 2z = 17; 3x + 20y ? z = ?18; 2x ? 3y + 20z = 25 (20)
Q4. Show that the transformation
1
1
z
w i
z
?
?
?
transform the circle | z | = 1 onto the real axis of
the w ? plane and the interior of the circle into the upper half of the w ? plane. (20)
Q5. Define Euler?s equation and find the shape of the curve of the given perimeter enclosing
maximum area. (20)
Q6. Discuss Hamilton?s principle and drive Lagrange?s equation. (20)


2 | M-36202 (S9)-500


Q7. State Parseval?s identity for fourier transforms. Prove that

2 2 2 2
0
( )( ) 2 ( )
dt
a t b t ab a b
?
?
?
? ? ?
?
(20)
Q8 .Determine the largest eigen value and the corresponding eigen vector of the matrix

2 1 0
1 2 1
0 1 2
A
? ? ?
? ?
? ? ?
? ?
? ? ?
? ?
(20)












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