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Numerical Methods for Partial Differential Equations

Slides/notes and Jupyter notebook demos for an introductory course of numerical methods for PDEs.

Originally developed for CS555 in the spring of 2020 in the Department of Computer Science at the University of Illinois, based on prior versions of the class taught by Luke Olson.

  • PDF of these slides/notes (see notes for source)

  • Demos in Binder

  • The demos use annotations for ipython-demo-tools. A #clear annotation at the beginning of a code cell allows the clear-marked-inputs subcommand of prepare-ipynb to remove the content of those input cells, maybe to use them for live coding in class. The #clear marks themselves can be removed by that remove-marks subcommand.

  • The notes are written in Org mode, which serves as a lightweight markup language over LaTeX. They're easiest to edit in Emacs, but vim-orgmode will do as well.

    To build the notes, you need any recent version of Emacs installed. Also make sure that submodules cloned properly:

    git submodule update --init

    Then simply change to the notes subdirectory and say:

    ./make.sh

    The script will optionally make use of latexrun. If you get

    There were errors; output not updated

    on the first go, simply rerun make.sh.

  • make.sh will generate two PDFs: notes.pdf and notes-folded.pdf. They differ in whether the boxes present in the notes (containing many of the most salient mathematical developments) are filled in or not.

    I use the un-filled version for class and fill in the boxes by hand during class using Xournal++ (but equivalent notetaking applications should work just as well).

Problems and Assignments

If you can demonstrate that you are teaching a related course at a college or university anywhere in the world, I have homework assignments and projects (some of which are autograded using the RELATE system) that I would be happy to share with you.

MIT License

Copyright (C) 2020 Andreas Kloeckner

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.