ما

a)

b)

a)

b)

a)

b)

0)

a)

b)

0)
a)
b)
0)

B4A0002

Find the Fourier cosine transform of
f(x) = x2, ifO
0, ifx>1
Find the Laplace transform of
(i) sinhtcost (ii) (t -1)°
Find the inverse Laplace transform of അത്തു
(s + v2)(s— v3)
Solve the initial value problem, using Laplace transforms.
y’+y’ + 9y =0, y(0) = 0.16, y’(0) =0

PART C (MODULES V AND VI)
Answer two full questions.

Using Newton Raphson Method Compute the square root of 51 correct to 4 decimal
places

For the following data calculate the value of y when x = 9

x: 8 10 12 14 16 18

y: 10 19 32.5 54 89.5 154

Given f(2) = 5, (2.5) =6, find the linear interpolating polynomial using Lagrange’s
formula and also find (2.2)

Determine the interpolating polynomial for the following data

x: -l 0 1 3

ys 2 1 0 -1 Hence find the value of y when x = 2

Solve the following by Guass — Seidel Method
67९ + 157 + 27 ८ 72

x +y+54z=110

27x + 6by—z=85

Evaluate [ _¢x_ , using Simpsons rule by taking step size h=1
0 1427

Using Euler Method, Solve y =x+ y, y(0)=1 for x =0.2

Find y(0.1) by improved Euler method given y = -xy’, y(0) = 2

Apply Runge — Kutta fourth order method to find an approximate value of y when
x= 0.1 given that. =x+yandy=1

when x 0

Ti KR

Page 2 of 2

(7)

(8)

(7)

(8)

(7)

(7)

(6)

(6)

(8)

(6)

(6)
(6)
(8)