PTU B.Tech Petroleum Engineering 3rd Semester May 2019 72158 ENGINEERING MATHEMATICS III Question Papers

PTU Punjab Technical University B-Tech May 2019 Question Papers 3rd Semester Petroleum Refinary Engineering

Roll No.
Total No. of Pages : 02
Total No. of Questions : 09
B.Tech. (Petroleum Refinery Engineering) (2013 Onwards) (Sem.?3)
ENGINEERING MATHEMATICS-III
Subject Code : BTAM-201
M.Code : 72158
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1.
SECTION-A is COMPULSORY consisting of TEN questions carrying T WO marks
each.
2.
SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3.
SECTION-C contains T HREE questions carrying T EN marks each and students
have to attempt any T WO questions.




SECTION-A
1.
Write briefly :

a) Can f (x) = sin (1/x), ? x be expanded in Fourier series?

b) Find the Laplace transform of f (t) = (sin t ? cos t)2.

c) Give the Laplace transform of Unit Impulse function.
s 3

d) Find the Laplace inverse of
.
2
s 6s 13

e) Find the singular point of the differential equation P0 (x) y + P1 (x) y + P2(x)y = 0.

f) Formulate the PDE from : z = ax + a2y2 + b.
3
z

g) Solve the PDE:
cos (2x 3y) .
2
x

y

1

h) Find the poles of : f (z)
.
(z 1) (z 2)

i) Show that the function u = e?x (x sin y ? y cos x) is harmonic.
2
z 2z

j) Find the residue of f (z)
at its poles.
2
z 4
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SECTION-B

1
2.
Find Fourier series expansion of f (x) = x2, ? < x < . Hence deduce
.
2
n
n
1
3.
a) Evaluate L {e?2tt cos t}.

1 s

b) Find Laplace inverse of log
.
s
4.
Find the power series solution of the differential equation (1 ? x2)y ? 2xy + 2y = 0 about
x = 0.
5.
Solve the PDE: (x2 ? y2 ? z2) p + 2xyq = 2xz.
cos x
6.
Find analytic function, whose real part is u
.
cosh 2 y cos 2x

SECTION-C
7.
a) Using Laplace transform, solve y + 2y ? 3y = sin t, given that y (0) = y(0) = 0.


x,
0 x


2

b) Expand f (x)
, as a half range sine series.

x,
x


2
8.
a) Solve the PDE: (mz ? ny) p + (nx ? lz) q = ly ? mx.

b) Find the image of the w-plane of the circle |z ? 3| = 2 in the z-plane.
2
u

u
9.
Solve the equation

subject to the conditions u (x, 0) = 3 sin nx, u (0, t) = 0 and
2
t

x
u (l,t) = 0, where 0 < x < l, t > 0.




NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.

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