OMCA101 COMPUTATIONAL MATHEMATICS

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Description

SESSION SPRING 2024 PROGRAM MASTER OF COMPUTER APPLICATIONS (MCA)

SEMESTER I

COURSE CODE & NAME OMCA101– COMPUTATIONAL MATHEMATICS

CREDITS 4

 

Assignment Set – 1ST

Questions

 

  1. Convert your birth year into binary system, octal system, and hexadecimal system and express the birth year in floating point base-10. (Show steps of conversion).

Ans: To convert a birth year (let’s use 1990 as an example) into the binary, octal, and hexadecimal systems, and express it in floating-point base-10, follow these steps: 

Binary Conversion Step-by-Step Conversion:  Divide the year by 2, noting the quotient and the remainder. Continue dividing the quotient by 2 until you reach 0.

The binary representation is

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  1. A. Define absolute error, relative error, and percentage error. Use an example of your own choice to calculate these errors.

Ans: Absolute Error, Relative Error, and Percentage Error are measures used to quantify the accuracy of a measurement or an approximation.

Here’s a brief explanation of each, along with a step-by-step example: 

Definitions Absolute Error: 

The difference between the measured or approximated value and the true value. Formula:

Absolute Error =

Measured Value –

 

  1. Use Newton’s Backward interpolation formula to compute f(45095) from the following data: (45000, 9.648583), (45020, 9.648696), (45040, 9.648810), (45060, 9.648923), (45080, 9.649036), (45100, 9.649150).

Ans:

To use Newton’s Backward Interpolation Formula, we need to compute the backward difference table and then apply the formula.

Here are the steps: 

Given Data:

 

Assignment Set – 2ND

Questions

 

  1. Find the root of the equation 3x- cos x – 1 =0, by Newton-Raphson method, correct up to 8-significant figures.

Ans: To find the root of the equation  3 − cos ⁡ − 1 = 0 3x−cosx−1=0 using the Newton-Raphson method, we proceed as follows: 

Function and Derivative:

Define the function and its derivative:

() = 3 − cos ⁡

 

 

  1. Solve by Gauss-elimination method, the system: x+2y+3z=10, x+3y-2z=7, 2x-y+z=5.

Ans: To solve the system of equations using the Gauss-elimination method, we start by representing the system in augmented matrix

 

  1. Verify Cayley-Hamilton theorem and compute the inverse of the matrix

A= [ ].

Ans:

To verify the Cayley-Hamilton theorem for the given matrix A and then compute its inverse, let’s proceed step by step. 

  1. Verifying Cayley-Hamilton Theorem

The Cayley-Hamilton theorem states that every square matrix satisfies its own characteristic equation. The characteristic equation of a matrix A is