PTU B.Tech Aerospace Engineering 3rd Semester May 2019 60537 MATHEMATICS III Question Papers

PTU Punjab Technical University B-Tech May 2019 Question Papers 3rd Semester AREO-Aerospace-Engineering

Roll No.
Total No. of Pages : 02
Total No. of Questions : 09
B.Tech. (Aerospace Engg.) (2012 Onwards)/(ANE) (Sem.?3)
MATHEMATICS ? III
Subject Code : AM-201
M.Code : 60537
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
Q1.
Answer briefly :

a) Find
2
L{
t
te sin 5 }
t .
4
s



e

b) Find
1
L
.
s 4



c) What is the value of Jn+1 (x) + Jn?1 (x) in terms of Jn(x)?

d) Write the complete solution of a differential equation when the roots of the indicial
equation are distinct and differ by an integer.

e) Form the partial differential equation from, z = f (x2 ? y2).

f) Solve
p q 1.

g) Write any one important property of analytic functions.

h) Give an example of a harmonic function.

i) Disucss Dirichlets conditions ?

j) Find the sine series of x2 in (0,1).
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SECTION?B
Q2.
Find the fourier series of x cos x in the interval (?, ).
Q3.
Using the concept of Laplace equations, solve

x + 9x = 6cos 3t where x (0) = 2, x(0) = 0.
1
Q4.
Show that J (x)
cos(n x sin )
d
n


0

Q5.
Solve, x(y2 ? z2) p + y (z2 ? x2) q = z (x2 ? y2)
Q6.
Determine the analytic function whose real part is
2
2
log x y
.

SECTION?C
Q7.
Solve in series, y + xy = 0.
Q8.
A tightly stretched string with fixed end points x = 0 and x = l is initially at rest in its
equilibrium position. If it is set vibrating by giving to each of its points a velocity
x (l ? x), find the displacement of the string at any distance x from one end at any time t.

cos3
Q9.
Evaluate by contour integration,
d

.
0 5 4 cos






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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