a)

b)

a)

b)

a)

b)

0)

a)

b)

0)
a)
b)
0)

84/0002
Find the Fourier cosine transform of
f(x) = 22,10 > > 1
0, ifx>1
Find the Laplace transform of
(i) sinhtcost (ii) ൧൧7

Fi ⋅ 1
ind the inverse Laplace transform of (൫൦൫

Solve the initial value problem, using Laplace transforms.
۳+ + 9950, 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 54 895 154

Given f(2) = 5. f(2.5)=6, find the linear interpolating polynomial using Lagrange’s
formula and also find 72.2)

Determine the interpolating polynomial for the following data

x : -1 0 1 3

y: 2 1 0 -1 Hence find the value of y when 2

Solve the following by Guass — Seidel Method
6x + 15422 ಎ72

x + y +54z=110

27x + 69 - 2 - 5

6 dx
Evaluate J; <>.

using Simpsons rule by taking step size h=1

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

Find y(0.1) by improved Euler method given ४ = -xy’, y(0) = 2

Apply Runge — Kutta fourth order method to find an approximate value of y when
+ = 0.1 given that = x ‏برج‎ and y = |

when x = 0

بد بد ‎॥‏

Page 2 of 2

(7)

(8)

(7)

(8)

(7)

(7)

(6)

(6)

(8)

(6)
(6)
(6)
(8)