Hello there! 👋 Welcome to the repository of Numerical Analysis. Here, you'll find various code files encapsulating my journey through the IPE-312 Numerical Analysis Lab. I've ventured into various topics, all coded using the versatile MATLAB, and to make the concepts crystal clear, I've provided MATLAB scripts for explanations. Let's dive into the specifics:

When equations meet algorithms! 🌱 In this section, I've tackled the fascinating realm of finding the roots of equations using multiple techniques. Each method has covered:

• Bisection Method (Bisection.mlx): A classical approach to narrowing down the root's range until precision is achieved.
• Graphical Method (Graphical_Method.mlx): Visualizing roots through graphs for a clearer understanding.
• Newton-Raphson Method (Newton_raphson.mlx): A powerful iterative technique to refine root approximations.
• Regula Falsi Method (Regula_Falsi_Method.mlx): A method that blends bisection with linear interpolation for quicker convergence.
• Secant Method (Secant.mlx): An iterative approach similar to Newton-Raphson but doesn't require derivative calculation.

Unveiling the art of optimization! 🎯 This section is all about the Golden Section Search, an optimization algorithm aimed at finding the extremum of functions

📊 Here, I've explored numerical integration methods to approximate definite integrals:

• Simpson's 1/3 Rule (Simpson_One_third_rule.mlx): Dividing and conquering integration intervals for accurate results.
• Simpson's 3/8 Rule (Simpson_three_eight_rule.mlx): A slight variation of Simpson's rule for even better accuracy.
• Trapezoidal Rule (Trapezoidal_rule.mlx): Approximating the integral using trapezoids – a classic approach.

📈 In this section, I've explored numerical differentiation using the Runge-Kutta 4th Order method, a popular choice for solving ordinary differential equations (ODEs).

🧩 This final section delves into LU decomposition, a technique that simplifies matrix operations.

This repository is a testament to my journey through IPE-312, capturing my efforts to make numerical concepts tangible through code.

Feel free to reach out if you have any questions, insights, or even code optimizations to share. 🚀🔢