Hi, welcome to my numerical analysis projects.

This repository contains a collection of Jupyter Notebook (.ipynb) files focused on numerical analysis techniques. Each notebook explores various computational methods for solving mathematical problems, with interactive code, explanations, and visualizations.

Table of Contents

• Overview
• Projects
• Requirements
• Installation
• Running the Notebooks
• Contributing
• License

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Overview

Numerical analysis focuses on developing algorithms to approximate solutions for problems in continuous mathematics. These Jupyter Notebooks explore a range of topics, including:

• Solving linear and nonlinear equations
• Numerical integration and differentiation
• Eigenvalue problems
• Approximation methods
• Differential equations and more

Each notebook provides code implementation, mathematical derivations, and visualizations to help users understand the underlying numerical methods.

Projects

Below are some of the topics covered in this repository:

1. Solving Linear Systems
2. Numerical Differentiation and Integration
3. Optimization and Root Finding
4. Sparse Matrices and Eigenvalue Problems
5. Approximation Methods
6. Numerical Solutions of Differential Equations

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Requirements

• Matplotlib: Used for visualization of data and results.
• NumPy: Used for numerical computations.
• Pandas: Used for data manipulation and analysis.
• Plotly: Used for interactive visualizations.
• SciPy: Used for advanced scientific computations, including optimization, integration, and sparse matrix operations.
• SymPy: Used for symbolic mathematics.
• IPython Widgets: Used for interactive elements.

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Installation

1. Clone the repository (or download the notebooks):

   git clone https://github.com/kyracho/numerical-analysis-projects.git
   cd numerical-analysis-projects

2. Set up a virtual environment (optional but recommended):

   python -m venv venv
   source venv/bin/activate  # On Windows use `venv\Scripts\activate`

3. Install the required packages:

   pip install -r requirements.txt

Alternatively, you can install the required packages manually:

pip install matplotlib numpy pandas plotly scipy sympy ipywidgets

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Running the Notebooks

To run the Jupyter Notebooks locally, follow these steps:

1. Launch Jupyter Notebook:

   jupyter notebook

2. Open the desired .ipynb file from the list in the Jupyter interface.

3. Interact with the code and visualizations. Many notebooks contain interactive widgets and plots, so be sure to run each cell and explore the outputs.