This assignment has eight problems of 40 marks, each of 5 marks. All problems are compulsory. 10 marks are for viva voce. Please go through the guidelines regarding assignments given in the programme guide for the format of presentation.

Note: The programs are to be written in C/C++ and/or in MS-Excel/Any spread sheet.

Q1. Write a program in C/C++ to find the solution of system of linear equations (given below), by suing Gauss- Elimination method:

𝑥 + 𝑦 + 𝑧 = 2

𝑥 − 2𝑦 + 3𝑧 = 14

𝑥 + 3𝑦 − 6𝑧 = −23

Q2. Write a program in C/C++ to determine the approximate value of the definite integral (I), by using Simpson’s (1/3)rd rule:

I = ∫ 𝑥 1/3 𝑑𝑥,

Using step size (ℎ) = 0.2 .

Q3. 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

Q4. Write a program in C/C++ to calculate the value of “cos 𝑥” by using the series expansion given below:

cos 𝑥 = 1 − 𝑥 2 2! + 𝑥 4 4! − 𝑥 6 6! + ⋯

Note: Evaluate cos 𝑥 only upto first three terms.

Also find the value of cos 𝑥 by using the inbuilt function.

Compare the results i.e., the result produced by your program and that produced by

inbuilt function. Based on comparison, determine error.

Q5. Write a program in C/C++ to find the root of the following equation by using “Bisection Method” :

Equation:

𝑥 3 − 5𝑥 + 1 = 0; 𝑥 ∈ [1, 2]

Q6. Write a program in C/C++ to approximate the value of Integral (I), by using Trapezoidal rule :

I = ∫ 𝑑𝑥 √5 + �

Q6. Write a program in C/C++ to approximate the value of Integral (I), by using Trapezoidal rule :

I = ∫ 𝑑𝑥 √5 + �

Using step size (ℎ) = 0.2 .

Q7. Write a program in C or C++ to demonstrate the operation of the following operations, for the function 𝑓(𝑥) = 𝑥 2 + 𝑥 + 7 ∶

(a) Forward Difference Operator

(b) Central Difference Operator

Q8. Write a program in C or C++ to calculate the value of 𝑒 𝑥 by suing its series expansion, given below :

𝑒 𝑥 = 1 + 𝑥 + 𝑥 2 2! + 𝑥 3 3! + ⋯

Note: Evaluate 𝑒 𝑥only upto first three terms.

Also find the value of 𝑒 𝑥 by using the inbuilt function and compare it with the result

produced by your program.