Introduction

Numerical Analysis is a branch of applied mathematics that provides methods to find approximate solutions when exact analytical solutions are not possible.
In many real problems, equations cannot be solved by simple algebra, especially when they are nonlinear.
In such cases, numerical methods are used to find values of ( x ) that satisfy:

$$ f(x) = 0 $$

where the root ( x ) represents the point at which the function crosses the x-axis.
These types of problems are common in engineering, physics, and computer science, where models are based on complex mathematical relationships.

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This project studies three important numerical methods for solving nonlinear equations:
Bisection, Newton–Raphson, and Secant.
Each of these methods uses an iterative process — starting from one or more initial guesses and improving them step by step until the result is close to the true root.

The main goals of this project are to: - Implement each method using GNU Octave (MATLAB-compatible software).
- Compare the methods in terms of speed of convergence, accuracy, and number of iterations.
- Relate the methods to practical applications in science and engineering.

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By completing this project, students gain a clearer understanding of how numerical algorithms work and why they are important in real-world problem solving, optimization, and simulation.
These methods show how mathematics can be applied using computers to solve problems that would otherwise be too difficult to handle analytically.