📉 Real Root-Finding Methods in MATLAB

This project applies numerical methods to find real roots of equations using both the Bisection Method and Newton's Method in MATLAB. It includes performance comparisons and visualizations of convergence speed across tolerances.

🧠 Methods Implemented

• Bisection Method
  Applies the Intermediate Value Theorem to iteratively narrow down an interval containing a root.

• Newton's Method
  Uses derivatives to iteratively estimate root convergence via tangent lines.

📊 Features

• Comparison of convergence speed between Bisection and Newton’s methods
• Visualization of:
  • Cooling rate vs bar length (from root calculations)
  • Iterations required vs tolerance (log-scale)
• Modular MATLAB functions with adjustable tolerances and ranges

📈 Key Concepts

• Root-finding for one-variable functions
• Convergence behavior and iteration count analysis
• MATLAB function handles (@), plotting, and iterative methods

🚀 How to Run

1. Open Project2.m in MATLAB
2. Ensure any function files (Bis, Newt) are in the same folder
3. Run:

Project2