Download PTU B.Tech 2020 March PE 3rd Sem Engineering Mathematics III Question Paper

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech PE (Petrolium Engineering) 2020 March 3rd Sem Engineering Mathematics III Previous Question Paper

1 | M-72189 (S2)- 191
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech.( Petroleum Refinary Engineering) (2013 Onwards) (Sem.?3)
ENGINEERING MATHEMATICS-III
Subject Code : BTAM-201
M.Code : 72189
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) Define Fourier series expansion for an even function.
b) Find Fourier sine series of the function f (x) = 1, 0 ? x ? 2.
c) Find the inverse Laplace transform of
( /2)
2
4
16
s
e
s
? ?
?

d) Find the Laplace transform of f (t) = t sin t.
e) Obtain a partial differential equation by eliminating the arbitrary constants c and ?
from z = ce
?t
cos ( ?x)
f) State and prove first shifting property of Laplace transforms.
g) Find singular points of the differential equation (1 ? x
2
) y ? ? ? 2xy ? + n (n + 1)y = 0
h) State Cauchy?s integral formula.
i) Show that the function u (x, y) = 2x + y
3
? 3x
2
y is harmonic.
j) Is f (z) = | z |
2
analytic function? Justify your answer.
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1 | M-72189 (S2)- 191
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech.( Petroleum Refinary Engineering) (2013 Onwards) (Sem.?3)
ENGINEERING MATHEMATICS-III
Subject Code : BTAM-201
M.Code : 72189
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) Define Fourier series expansion for an even function.
b) Find Fourier sine series of the function f (x) = 1, 0 ? x ? 2.
c) Find the inverse Laplace transform of
( /2)
2
4
16
s
e
s
? ?
?

d) Find the Laplace transform of f (t) = t sin t.
e) Obtain a partial differential equation by eliminating the arbitrary constants c and ?
from z = ce
?t
cos ( ?x)
f) State and prove first shifting property of Laplace transforms.
g) Find singular points of the differential equation (1 ? x
2
) y ? ? ? 2xy ? + n (n + 1)y = 0
h) State Cauchy?s integral formula.
i) Show that the function u (x, y) = 2x + y
3
? 3x
2
y is harmonic.
j) Is f (z) = | z |
2
analytic function? Justify your answer.
2 | M-72189 (S2)- 191
SECTION-B
2. Find the solution of the given homogeneous partial differential equation
[D
3
? 3D
2
D ? + 3D(D ?)
2
+ (D ?)
3
]z = 0.
3. Show that the function :
3 3
2 2
(1 ) (1 )
0,
( )
0 0
x i y i
z
f z x y
z
? ? ? ?
?
?
? ?
?
?
?
?

satisfies the Cauchy Riemann equations at z = 0 but f ?(0) does not exist.
4. Evaluate the integral
2 3
,
( 1)
z
C
e
dz
z z ?
?
?
C : | z | = 2
5. Find inverse Laplace transform of
2 2
1
( 9) s ?

6. Express the Bessel?s function J
4
(x) in terms of J
0
(x) and J
1
(x).

SECTION-C
7. Find series solution about x = 0, of the differential equation
x (1 + x) y ? ? + 3xy ? + y = 0
8. Find all possible Taylor and Laurent series expansions of the function
f (z) =
2
1
( 1)( 2) z z ? ?

9. Find the Fourier series expansion of the function :
2
0 0
( )
0
x
f x
x x
? ? ? ? ?
?
?
? ? ?
?

and hence show that
2
2 2 2
1 1 1
1 ...
2 3 4 6
?
? ? ? ?

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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