Applied Mathematics in Python

This repository contains a collection of projects in applied mathematics implemented in Python. The projects cover various topics such as fractals, heat transfer and ferromagnetics simulations, and nonlinear dynamics.

Projects

1. Julia Set Fractal: Given a mapping generates a corresponding Julia fractal that you can interactively explore.
2. Heat Transfer Simulation: Simulate heat transfer scenarios using diffusion equations.
3. Ferromagnetics Simulation: Calculates Mean Energy of a ferromagnetic using Ising's model.
4. Boids Simulation: Simulates behavior of a flock of "birds" by applying 3 simple rules: separation, cohesion and alignment.
5. Nonlinear Dynamics Graphs:
   • Bifurcation Diagrams: Visualizes the behavior of nonlinear systems as parameters change.
   • Mapping Diagrams: Mappps the evolution of a given discrete dynamic system.
   • Lyapunov Exponent Graphs: Analyze the stability of chaotic systems.
6. Numerical Methods: Implementaion of various numerical methods to solve different problems in mathematics.

About the Author

This project is the work of Nikita Tkachenko, a student at Higher School of Economics during the academic years 2023-2024.

Installation Guide

Requirements

• Python (>=3.6)
• Jupyter Notebook
• Each projects' requirements are listed in corresponding requirenemets.txt files.

Steps

1. Clone the repository:

   git clone https://github.com/tka4nik/Applied_Mathematics_Python.git
   cd applied-mathematics-python

2. Create a virtual environment (optional but recommended):

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

3. Install dependencies:

   pip install -r <choosen_project_ditectory>/requirements.txt

4. Launch Jupyter Notebook:

   jupyter notebook

License

This project is licensed under the MIT License.