a)

b)

a)

b)

०)

8)

०)

९)

2)

b)

02000M A202052001

1 if |x|<1

0 {|| > 1 Hence show (மர்‌

Find the Fourier Transform of f(x) =|

5 — da = ்‌
Solve using Laplace Transform: y" — 3y’ + 29 = 4 given y(0) = 2,)'(0) = 3

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

Using Lagrange’s interpolation formula, find a parabola of the form y = ax? +
bx + ८ passing through the points (0,0), (2,4) and (3,12)

Using Newton-Raphson Method, find the real root lying between 0 and 1 of
3x - cosx — 1 = 0. (Correct to three decimal places)

Apply Lagrange’s interpolation formula to find y at x = 2 for the following values
for y = f(x). Given f(0) = -12,/(1) = 0, f (3) = 6 and f(4) = 12.

Solve by Gauss Elimination Method:

3x + 4y + 52 = 18, 2x - 9 + 82 = 13, 5x - 29 + 72 = 20.
Evaluate [ = [ന using (i) Trapezoidal Rule (ii) Simpson’s = Rule (Take
h=1). Also find the value of the integral by actual integration.

Using Euler’s Method compute the value of y(0.1) given y’ =x +5 , (0) = 1

(Take h = 0.025)
Using Newton’s Interpolation Formula find f(1.2)and f (2.0) from the table.

Using Runge — Kutta Method of 4% order, find y(0.8) correct to four decimal

places ir? = y—x? given y(0.6) = 1.7379 (Take ಗಿ = 0.1)

Page 2 of 2

10

10