Code No: 154BG R18
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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
B.Tech II Year II Semester Examinations, March - 2022
LAPLACE TRANSFORMS, NUMERICAL METHODS AND COMPLEX VARIABLES
TU
(Common to EEE, ECE, EIE)
Time: 3 Hours Max. Marks: 75
Answer any five questions
All questions carry equal marks
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3t
1.a) Find the Laplace transform of t e cos 2t
s2
b) Find L1 2
[7+8]
U
s 4 s 13
se
sin 2t
2.a) Find the laplace transform of
t
d2x dx
b) Using Laplace transform solve the differential equation 2 x et , given that
dP
2
dt dt
x(0) 2, x '(0) 1 [7+8]
3.a) Find a real root of x log10 x 1.2 0 correct to four decimal places using Regula falsi
a
method.
pe
b) Use Newton’s Backward difference formula to find y(9). [8+7]
x 2 5 8 11
y 94.8 87.9 81.3 75.1
rs
4.a) Find y(43) if y(20) = 0.939, y(25)=0.906, y(32) = 0.848 and y(49) = 0.56 using
Lagrange’s interpolation formula.
M
b) Using Regula-falsi method, solve x 2 2 x 4 0 for a negative root. [8+7]
ar
1
dx
5.a) Evaluate using: i) Trapezoidal rule ii) Simpson’s 1/3rd rule by taking h=0.25.
0
1 x 2
ch
dy
b) Find y(0.1) and y(0.2) using Taylor series given that x y, y (0) 1 [7+8]
dx
Find the analytic function whose real part is e x x sin y y cos y
20
6.a)
b) Evaluate y 2
xy 3x 2i dz Where C is the straight line from z=0 to z=1+i. [7+8]
C
2
1
7.a) Find the Laurent series for f(z)= z 2e z about z=0.
2
b) Evaluate 3 dz where C is z 2 . [8+7]
z ( z 4)
C
ez
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8.a) Using Cauchy’s integral formula evaluate
C
z 1 z 1dz
2
whose C is the circle
z 2.5 .
TU
z 3dz
b) Evaluate using Residue theorem
C
( z 1)2 ( z 3)
where C is z =2. [8+7]
H
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U
se
dP
a pe
rs
M
ar
ch
20
2 2
