chicolucio/integrals

Computing integrals

Integrals

A Python project to compute integrals:

• symbolically with SymPy
• numerically through Riemann sums

The project aims to be educational, showing how numerical integration works through animations like the one at the beginning. There are more animations in the images folder. Yes, you can do such calculations with SciPy but without the nice animations :-)

Usage

1. clone the repo, not a package yet :-(
2. create a virtual environment with Python 3.8+
3. activate the virtual environment
4. install dependencies
5. run the scripts

git clone https://github.com/chicolucio/integrals
cd integrals
python -m venv .venv
source .venv/bin/activate
pip install -r requirements.txt
python animation.py
python integral.py
python antiderivatives.py

animation.py shows how more Riemann rectangles make the approximation better. integral.py has examples of how to use the other methods. Both files have more examples that can be uncommented in the code as instructed in them. antiderivatives.py just plots a family of functions that are antiderivatives of 2x.

Testing

Tests can be run in the top-level directory with the command pytest -v tests/.

Contributing

All contributions are welcome.

Issues

Feel free to submit issues regarding:

• recommendations
• more animations or examples
• enhancement requests and new useful features
• code bugs

There are some open issues waiting for your help, see here.

Pull requests

• before starting to work on your pull request, please submit an issue first
• fork the repo
• clone the project to your own machine
• commit changes to your own branch
• push your work back up to your fork
• submit a pull request so that your changes can be reviewed

License

MIT, see LICENSE

Citing

If you use this project in a scientific publication or in classes, please consider citing as

F. L. S. Bustamante, Integrals, 2022 - Available at: https://github.com/chicolucio/integrals

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integrals's Issues

Add trapezoid rule

Add methods to compute and plot using the trapezoidal rule.

Hint: "The trapezoidal rule may be viewed as the result obtained by averaging the left and right Riemann sums, and is sometimes defined this way."

Add Simpson's rules

Add methods to compute and plot using the Simpson's rules.

Hint: There is a simple form based on trapezoidal rule and Riemann's midpoint.

Port to Streamlit