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bmstu_2_sem_differential-equations

Overview

This repository contains several Python scripts and Jupyter notebooks for numerical analysis and solving differential equations. The tools included are focused on Fourier series, solving second-order ordinary differential equations (ODEs), and using the Euler method for ODEs. Additionally, there is a script for modeling uranium decay.

Files

1. Fourier Series (5.ipynb)

  • Description: This Jupyter notebook is designed to generate and plot Fourier series.
  • Contents:
    • Import statements for necessary libraries (numpy, matplotlib.pyplot).
    • A class FourierSeries that includes methods for initializing parameters and generating the series.
  • Usage: Open the notebook in Jupyter and run the cells to see the implementation and plots.

2. Second-Order ODE Solver (13.ipynb)

  • Description: This notebook provides a numerical solution for second-order ODEs.
  • Contents:
    • Import statements for numpy and matplotlib.pyplot.
    • A class SecondOrderODESolver that includes methods to set up and solve the differential equations.
  • Usage: Open the notebook in Jupyter and follow the provided steps to solve second-order ODEs.

3.Second-Order ODE Solver (12.ipynb)

  • Description: This notebook provides a numerical solution for second-order ordinary differential equations (ODEs) using the Runge-Kutta 4th order (RK4) method.
  • Contents:
    • Import statements for numpy and matplotlib.pyplot.
    • A class SecondOrderODESolver that includes methods to set up and solve the differential equations.
  • Usage: Open the notebook in Jupyter and follow the provided steps to solve second-order ODEs.

4. Euler Method (Euler method.ipynb)

  • Description: This notebook explains and implements the Euler method for solving ODEs.
  • Contents:
    • Markdown cells with explanations of the Euler method.
    • A class Euler with methods to implement the Euler method.
  • Usage: Open the notebook in Jupyter to read the explanations and run the code cells to see the Euler method in action.

5. Uranium Decay Solver (mathmodel.py)

  • Description: This Python script models the decay of uranium using a numerical approach.
  • Contents:
    • Import statements for numpy and matplotlib.pyplot.
    • A class UraniumDecaySolver with methods to simulate uranium decay over time.
  • Usage: Run the script in a Python environment to simulate uranium decay and generate plots.

Getting Started

To use the notebooks and scripts in this repository, follow these steps:

  1. Clone the repository:

    git clone <repository_url>

  2. Install the necessary packages: Ensure you have numpy and matplotlib installed. You can install them using pip:

    pip install numpy
pip install matplotlib

  3. Run the notebooks:

    • Open Jupyter Notebook or JupyterLab.
    • Navigate to the directory containing the cloned repository.
    • Open the desired .ipynb file and run the cells sequentially.

  4. Run the Python script:

    • Execute the mathmodel.py script in a Python environment: 
      python mathmodel.py