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https://github.com/rxyalxrd/bmstu_2_sem_differential-equations

Solution of differential equations by numerical methods at the 2nd year of Bauman Moscow State Technical University.
https://github.com/rxyalxrd/bmstu_2_sem_differential-equations

jupyter-notebook python3

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Solution of differential equations by numerical methods at the 2nd year of Bauman Moscow State Technical University.

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README 

        
# 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**:

   ```sh

   git clone 

   ```



2. **Install the necessary packages**:

   Ensure you have `numpy` and `matplotlib` installed. You can install them using pip:

   ```sh

   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:

     ```sh

     python mathmodel.py

     ```