Course Code: BCSL-058

Course Title: Computer oriented Numerical techniques Lab Assignment

Number : BCA(5)/L-058/Assignment/2019-20

Maximum Marks: 50

Weightage: 25%

Last Dates for Submission: 15th October 2019 (For July 2019 Session)

15th April 2020 (For January 2020 Session

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 program guide for the format of the presentation.

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

Q1.

Write a program in C/C++ to find the solution of a system of linear equations (given below), by using 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=∫𝑥1/3 𝑑𝑥,1.00.2

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:

cos𝑥=1−𝑥22!+𝑥44!−𝑥66!+⋯

Note: Evaluate cos 𝑥 only up to the 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 the inbuilt function. Based on the comparison, determine the error.

Q5.

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

Equation:

𝑥3−5𝑥+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+𝑥10.2

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)=𝑥2+𝑥+7∶

(a) Forward Difference Operator

(b) Central Difference Operator

Q8.

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

𝑒𝑥=1+𝑥+𝑥22!+𝑥33!+⋯

Note: Evaluate 𝑒𝑥only up to the first three terms.

Also, find the value of 𝑒𝑥 by using the inbuilt function and compare it with the result produced by your program.