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. a. Find the Fourier transform of f(x)= | if < (7)
0 otherwise
b. Find the Laplace transforms of the following
i) cos t—tsint 10) 4/൦ (8)
. a. Find the inverse Laplace transform of the following
i) il)
2941 (25 - 10) , +,
52 + 2545 ಈ (8)
0. 8०५८ "+ 21# + 5 = 25/ »(0)--2 ந1(0)--2 using Laplace transforms (7)
PART C (MODULES V AND V1)
Answer two full questions.
. Solve f(x)=x—0.5cosx = 0 near = 0 by fixed point iteration method. (7)
b. Solve f (x)= 2x—cosx=0 by Newton Raphson’s method (7)
c. Find (9.2) from the values given below by Lagrange’s interpolation formula
x 8 9 95 11
f(x) 2.197225 2251292 2.397895 2079442 (6)

. a. Given (xj, f0q)) = (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 0.6rtusin g Newton's interpolation formula. (10)
b. Solve 10x, +x, +x, =6, x, +10x, +x, =6, x, +x, +10x, =6 by Gauss-Seidel
iteration method starting at x, =1 x, =land x, =| correct to 4 digits. (10)

1
| . , 1 ; 598
. a. Evaluate | ,dx with 4 subintervals by Simpson’s rule and compare it with the
+x"

0
exact solution. (7)
४. 8०५९ ‰ = # , 40) = 109 Euler method to find A!) with ಎ02 (7)
c. Solve 1൮ y(0)=Oby fourth order Runge-Kutta method with h = 0.1, 5
steps. (6)
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