Download PTU B.Tech 1st Semester [2019] 70970 ENGINEERING MATH III Question Papers

Download PTU (Punjab Technical University) B.Tech 1st Semester [2019] 70970 ENGINEERING MATH III Latest Question Paper

Roll No.
Total No. of Pages : 02
Total No. of Questions : 09
B.Tech. (EE) PT (Sem.?1)
ENGINEERING MATH-III
Subject Code : BTAM-301
M.Code : 70970
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 & C. have FOUR questions each.
3.
Attempt ANY FIVE questions from SECTION B & C carrying EIGHT marks each.
4.
Select atleast T WO questions from SECT ION - B & C.


SECTION-A
1. Solve the following :

a) Find half range cosine series for x in (0, ).

b) State Dirichlet's condition for expansion of a function in terms of Fourier Series.

c) If L (f(t)) = F(s) then prove that L (f(at) = F(s/a)/a.

d) Find laplace transform of e?2t sin2t.
2
d y
1 dy
1

e) Find the solution of

3
y 0 in terms of Bessel's function
2

2
dx
x dx
4x

f) Define regular singular and irregular point of a second order Linear differential

equation.
1


g) Form the Partial Differential Equation corresponding to
2
z y 2 f
log y


x


h) Solve the partial differential equation (z ? y) p + (x ? z) q = y ? x,
z

z

where p
, q

x
y



i) Is the function u = 2xy + 3xy2 ? 2y3 harmonic? Given reason.
z

j) Find the poles and residue at the poles of
.
cos z
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SECTION-B
2. Find Fourier series for f (x) = | sin x |, ? x .
3. State and prove second shifting theorem and hence find inverse Laplace transform of
2s

e
s



2

(s s 1)


4. Solve the homogeneous partial differential equation
2
2
2
z
z
z
4
4
4 sin (2x y).
2
2
x

x
y

y

2 sin x

5. Prove that J
(x)
cos x
1/2


x
x


SECTION-C
x
6. If f (z) = u + iv is an analytic function. Find f (z) if u v
, f (1) 1

2
2
x y
7. Find series solution of the differential equation
2
d y
dy
9x (1 x)
12
4 y 0.
2
dx
dx
8. A tightly stretched elastic string with fixed end points x = 0 and x = l is initially in a position given
x

by
3
y y sin
. If it is released from rest from this position find the displacement
0


l
y(x, t).
9. a) Using Residue theorem, evaluate the integral
(z 3)


,

where C is the circle | z | = 3
2
(z 1) (z 2)
C
z

b) Prove that w
maps the upper half of the z-plane into the upper half of w-plane.

i z

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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