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52031 Pages: 2

kx if 0
Find the Fourier transform of f(x) = € £ >> , ८ > 0.
0 if x>0

Find the inverse Laplace transform of ‏بے ے2 _ ۔‎ using Convolution
(൦ +1)(s~ +25)

Theorem.

Find the Laplace transforms of (i) t e“ (ii) cos(wt + 9)

Solve the initial value problem 1“ -- 1" - 6) = 0 , 1(0) = 6 ,1"(0) = 13 by using

Laplace transforms.

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

Find the positive solution of 2sinx=x by using Newton-Raphson method, the
solution is near to 2.

Calculate the Lagrange polynomial p(x) for the 4-D values of the function f(x),
f (1.00) = 1.0000, (1.02) = 0.9888, / (1.04) = 0.9784 ,and from it find the
approximate value of f(x) at x = 1.005.

Compute /(1.5) from /(1) = -1, /(2) = -[, / (3) = 1, /(4) = 5 by using Newton’s
forward interpolation formula.

Solve 6% + 2) + 8, = 26, 3x, + 52 + 23 = 8, 8x,+2x,=-7 by Gauss
Elimination method.

Find the value of (13)''*

using Newton Raphson method.
1
Evaluate eva by Trapezoidal rule taking 10 subintervals.
0
Use Euler’s method with h=0.1,compute the value of (0.5) for the equation
1" = ‏,2(د+ی)‎ y(0)= 0.
Use Runge-Kutta method with ‏ط‎ = 0.1, compute the value of 1(0.1) for the
equation y’ = xy, y(0)=1.
1
Evaluate |
0
exact solution.

dx

0095 xX

by Simpson’s rule taking 10 subintervals and compare it with the

KKK

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