SASTRA University 2009 B.Tech Computer Science and Engineering Transforms and complex variables 1 Mid Sem -2010 - Question Paper

SASTRA University
School of computing
B.tech CSE
First Mid Sem third semester
Transforms and Complex Analysis

Time 90min.

Part A 5*2=10
Part B 4*10 = 30
MM:50

Part A

1.Define Laplace Transform & state its conditions for existence.

2.Find L[sin3tsin2t]

3.Find L[e-3tsint2]

4. obtain the inverse transform of s/((s-b)2 + a2).

5.State the convolution of 2 function f(t) and g(t).

Part B
1. obtain Laplace inverse of
a).s+3/(s2 + 6s +13)2
b). s2/(s2 + a2)(s2+b2)

2.Find Laplace transform and inverse of 1-cost/t and log[1 + w2/s2] respectively.

3.a).By using convolution the Inverse Laplace transform of 1(s2+4)2.
b).Solve y'' + 4y'-5y =5 provided that y=0, dy/dt=2 at t=0.

4.a) Solve dy/dt-2x + 3y = 0 , dy/dt – y +2x = 0 with x(0) = eight , y(0) = 3
b) Evaluate (The integral is provided as an attachment To this Paper)

J te ²ⁱsintdt

0

Attachment: sastra-university-2009-b-tech-computer-science-and-engineering-4517-1.JPG

Earning:   Approval pending.