Download PTU B-Tech ECE 2020 Dec 3rd Sem 56071 Engineering Mathematics Iii Question Paper

Download PTU (I.K.Gujral Punjab Technical University (IKGPTU)) B-Tech (Bachelor of Technology) (ECE)-Electronics And Communications Engineering 2020 December 3rd Sem 56071 Engineering Mathematics Iii Previous Question Paper

Roll No.
Total No. of Pages : 02
Total No. of Questions : 18
B.Tech. (CE)/(ECE)/(Electrical Engineering & Industrial Control)/
(Electronics & Computer Engg)/(Electronics & Electrical) (2012 to 2017)/
(Electrical & Electronics) (2011 Onwards)/(EE) (2012 Onwards)
(Sem.?3)
ENGINEERING MATHEMATICS ? III
Subject Code : BTAM-301
M.Code : 56071
Time : 3 Hrs. Max. Marks : 60
INST RUCT IONS T O CANDIDAT ES :
1 .
SECT ION-A is COMPULSORY cons is ting of TEN questions carrying TWO marks
each.
2 .
SECT ION-B c ontains F IVE questions c arrying FIVE marks eac h and s tud ents
have to atte mpt ANY FOUR questio ns.
3 .
SECT ION-C contains THREE questions carrying T EN marks e ach and s tudents
have to atte mpt ANY TWO questions .
SECTION-A
Solve the following :
1.
Find Laplace transform t e?4t sin 3t.
3s 2
2.
Find inverse Laplace transform of
.
3
(s 3)
3s
e
3.
Find inverse Laplace transform of
.
s 2
1
2
4.
Using the value of

, show that J (x)
sin .
x
2
1
x
2
5.
Express 3x2 + 5x ? 6 in terms of Legendre polynomials.
6.
Derive a PDE by eliminating the arbitrary constants a and b from the equation x2 + y2 + (z
? b)2 = a2.
7.
Solve PDE (D2 + DD' ? 2 D'2) z = 0.
8.
Show that the function f (z) = z does not have derivative at any point.
9.
If f (z) is an analytic function with constant modulus then f (z) is constant.
10. State Cauchy's Integral Formula.
1 | M-56071
(S2)-193

---

SECTION-B
11. Find the Fourier series expansion of the function f (x) = x + , ? < x < . Hence show

1
1
1
that
1
......
4
3
5
7
12. Find the solution of the initial value problem using the Laplace transform
y + 6y + 13y = e?t , y (0) = 0, y (0) = 4.
13. Find two linearly independent solutions of the differential equation
2x2 y + x y ? (x2 + 1) y = 0, using Frobenius method.
14. Find the general solution of the partial differential equation (y + z) p + (x + z) q = x + y.
(z 1)
15. Evaluate
dz,
C : | z ? 3 | = 2.
3
z (z 2) (z 4)
C
SECTION-C
1
,
0 x 1
16. a) Write the Fourier cosine series of f (x)
.
1, 1 x 2
b) Let f (t) be a piecewise continuous function on [0, ], be of exponential order and
T
1
periodic with period T. Then L [ f (t) ]
st
e
f (t) dt.
1
sT
e
0
17. a) State and Prove Rodrigue's Formula.
b) Using the method of separation of variables, solve
u
u
3
2
u, u ( ,
x 0) 6 x
e
x
y
1
18. Find all Taylor and Laurent series expansions of f (z) =
about the point
2
(z 1) (z 2)
z = 1.
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.
2 | M-56071
(S2)-193

---