B4A001

1 if |x{<1

. a. Find the Fourier transform of f(x)=
0 otherwise

b. Find the Laplace transforms of the following

i) cos t—tsint ii) 40 ८7
. a. Find the inverse Laplace transform of the following
i) ii)
2s+1 (2s - 10)
82೨4245 $

४. Solve മാ" + 59 = 254 y (0) = 72, 2 (0)--2 using Laplace transforms

PART C (MODULES V AND VI)

Answer two full questions.

. a. Solve f (x) = + 0.5 008४ =0 near x = 0 by fixed point iteration method.

b. Solve f(x)= 2x-—cosx=0 by Newton Raphson’s method

x 9 9.5 11
‏)مر‎ ೩197225. 2.251292 2.397895 2.079442

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c. Find f (9.2) from the values given below by Lagrange’s interpolation formula
8

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. a. Given (x - (0.2, 0.9980), (0.4, 0.9686), (0.6, 0.8443), (0.8, 0.5358), (1,0),

find f(0.7) based on 0.2, 0.4, and 0.6 using Newton’s interpolation formula.

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b. Solve 10x, +x, +x, = 6, x,+10x, +x, = 6, x, +x, + 1093 = 6 by Gauss-Seidel

iteration method starting at x, ಎ1, x, = 184 x, =1correct to 4 digits.

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1
1
. a. Evaluate | ಇಫ್‌ with 4 subintervals by Simpson’s rule and compare it with the
120

exact solution.

b.Solve ¬" = +, (0) =1 by Euler method to find 211) with h=0.2

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९. Solve = 1 + 12, 1(0) = 0४४ fourth order Runge-Kutta method with ॥ = 0.1, 5

steps.

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