Download PTU B.Tech 2020 March ME 4th Sem Mathematics III Question Paper

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech ME (Mechanical Engineering) 2020 March 4th Sem Mathematics III Previous Question Paper

1 | M-54035 (S2)-2793
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech. (ME) (Sem.?4)
MATHEMATICS-III
Subject Code : AM-201
M.Code : 54035
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.

SECTION-A
1. Write briefly :
a) Give Dirichlet?s conditions for the Fourier series expansion of f (x).
b) Find the value of a
n
in the Fourier series expansion of f (x) = x, ? ? ? ? x ? ?.
c) Find Laplace transform of f (t) = t
n
.
d) Write the definition of unit step function.
e) Write the Laplace tansform of periodic function f (t) with period T.
f) Find the complementary function of PDE : (2D
2
+ 5DD ? + 2D ?
2
) z = 0.
g) Form the partial differential equation from z = ax + a
2
y
2
+ b.
h) Give definition of singular point.
i) Give definition of conformal mapping.
j) Evaluate ?[(x
2
+ 2y) dx + (3x ? y)dy] along the curve x = 2t, y = t
3
+ 3 between (0, 3),
(2, 4).

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1 | M-54035 (S2)-2793
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech. (ME) (Sem.?4)
MATHEMATICS-III
Subject Code : AM-201
M.Code : 54035
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.

SECTION-A
1. Write briefly :
a) Give Dirichlet?s conditions for the Fourier series expansion of f (x).
b) Find the value of a
n
in the Fourier series expansion of f (x) = x, ? ? ? ? x ? ?.
c) Find Laplace transform of f (t) = t
n
.
d) Write the definition of unit step function.
e) Write the Laplace tansform of periodic function f (t) with period T.
f) Find the complementary function of PDE : (2D
2
+ 5DD ? + 2D ?
2
) z = 0.
g) Form the partial differential equation from z = ax + a
2
y
2
+ b.
h) Give definition of singular point.
i) Give definition of conformal mapping.
j) Evaluate ?[(x
2
+ 2y) dx + (3x ? y)dy] along the curve x = 2t, y = t
3
+ 3 between (0, 3),
(2, 4).

2 | M-54035 (S2)-2793
SECTION-B
2. Find the Fourier series expansion of
1, 0
( )
2, 2
x
f x
x
? ? ? ? ?
?
?
? ? ? ?
?
.
3. i) Find L {t sin at} ii)
2
1
3
3 4 s s
L
s
?
? ?
? ?
? ?
? ?
.
4. Prove the recurrence relation
1
[ ( )] ( )
n n
n n
d
x J x x J x
dx
?
? for Bessel function.
5. Solve the linear partial differential equation (mz ? ny) p + (nx ? lz)q = ly ? mx.
6. Check if the function f (z) = 2xy + i (x
2
? y
2
) is analytic ?

SECTION-C
7. a) Find the half range Fourier cosine series expansion of f (x) = x, 0 < x < ?.
b) Find
1
1
( 2)( 1)
L
s s
?
? ?
? ?
? ?
? ?
using convolution theorem.
8. a) Solve the differential equation
3
2 , (0) 1
t
dy
y e y
dt
?
? ? ? using Laplace transform.
b) Solve (D
2
+ 4DD ? ? 5D ?
2
) z = sin (2x + 3y).
9. a) Find the analytic function, whose real part is
sin 2
cosh 2 cos2
x
u
y x
?
?
.
b) Find the Taylor?s series expansion of
1
( )
( 1)( 3)
f z
z z
?
? ?
for the region | z | < 1.


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