Ques 1.

Write a C/C++ program that implements (Do not use pivot condensation) Gaussian elimination
method for solving n linear equations in n variables, that calls procedures (5)
(i) Exchange of rows
(ii) lower-triangularisation and
(iii) back substitutions
 (Codes of procedures are also to be written)

Ques 2.

Use the program for solving the following system of linear equations:
2x + y + z = 7
3x + 2y + 3z = 16
4x + 5y + 3z = 23

Ques 3.

Write a program in C/C++ to find the root of the following equation by using “Bisection Method”. Equation:

Ques 4.

Write a C/C++ program that approximates a root of the equation f(x) = 0 in an interval [a, b] using Newton-Raphson method. The necessary assumptions for application of this method should be explicitly mentioned. Use the method to find one root of the equation: x3 + 4x2 - 19=0.

Ques 5.

Write a C/C++ program that approximates the value of a definite integral ∫

Ques 6.

Write a C/C++ program that approximates the solution of the initial value problem: y’ = f(t, y) with y(a) = y0 over [a, b] using Euler’s method. Using the program approximate the solution of the initial value problem: y’ = -2ty2 with y(0) =1

Ques 7.

Write a program in C/C++ to find the value of Sin(π/6) by using Lagrange’s Interpolation, the related  data is given below 
x: 0 π /4 π/2
y = Sin(x): 0 0.70711 1.0

Ques 8.

Write a program that approximates the value of a definite integral ∫