This repository provides a user-friendly GUI application built with CustomTkinter for performing numerical analysis tasks, specifically solving linear systems and numerical integration.

It offers functionalities for:

• Solving Linear Systems (Ax = B):
  • Inverse of A: Computes the exact solution using the matrix inverse.
  • Gaussian Elimination: Solves the system using forward and backward substitution after LU decomposition.
  • LU Decomposition: Factors the coefficient matrix (A) into a lower triangular matrix (L) and an upper triangular matrix (U) for efficient solution.
  • Cholesky Decomposition (for positive definite A): Exploits the positive definite nature of the matrix for a more efficient solution process.
• Numerical Integration:
  • Trapezoidal Rule: Approximates the definite integral of a function using trapezoidal segments.
  • Simpson's Rule: Provides a more accurate approximation compared to the trapezoidal rule using parabolic segments.

• Intuitive GUI: Easy-to-use interface for inputting matrices, vectors, functions, and integration limits.
• Clear Output: Presents solutions and integration results in a structured format.
• Customization: Supports adjustments to matrix/vector dimensions and integration parameters.

Prerequisites and Dependencies:

• Python (assumed to be installed)
• CustomTkinter
• NumPy
• NumExpr
• Pillow

1. Clone this repository:

git clone https://github.com/AkramOM606/Numerical-Analysis-GUI.git

2. Install the additional dependencies if not present:

pip install -r requirements.txt

3. Launch the application using Python

python main.py

The application features a user-friendly interface that allows you to directly interact with its functionalities. Simply launch the application and explore the available options within the GUI. The intuitive design guides you through matrix/vector input, method selection, and function/integration parameter specification.

We welcome contributions to enhance this project! Here's how you can participate:

1. Fork the repository.
2. Create a new branch for your feature or bug fix.
3. Make your changes and commit them.
4. Open a pull request to propose your changes.

We'll review your pull request and provide feedback promptly.

This project is licensed under the MIT License: https://opensource.org/licenses/MIT (see LICENSE.md for details).