Jupyter Notebook in Teaching

One self-contained Jupyter notebook for a 60-minute session on Jupyter Notebook, its use in teaching, and how AI can help prepare teaching material. It runs on an ordinary laptop CPU.

Main file: Jupyter_in_Teaching_FEM_and_PINNs.ipynb

Part	Content
1	Introduction to Jupyter Notebook: what Jupyter is, front-end / server / kernel, getting started, cells and shortcuts, Markdown and LaTeX, kernel state and hidden-state pitfalls, rich output and magics, notebooks in teaching, AI assistance for preparing notebooks
2	Finite elements for the 1D heat equation: weak form, P1 elements in space (method of lines, mass and stiffness matrices), backward Euler and Crank-Nicolson in time, stiffness and the explicit stability limit, snapshots, an animation and a space-time plot of the solution, and L2 / H1 error analysis with convergence studies in space and time
3	Physics-informed neural networks for the 2D Navier-Stokes equations: what PINNs are, the incompressible Navier-Stokes equations and Kovasznay flow, PyTorch essentials, implementing and training a PINN (Adam + L-BFGS), visualization and validation

The notebook starts with a contents list; the references for all three parts are collected at the end. Each part runs on its own after the Setup cells, so you can also jump directly to Part 2 or Part 3.

Setup (once)

Option A: conda (Anaconda, Miniconda or Miniforge)

conda env create -f environment.yml
conda activate jshare
jupyter lab

Option B: pip + virtual environment

python -m venv jshare-env
source jshare-env/bin/activate        # Windows: jshare-env\Scripts\activate
python -m pip install -r requirements.txt
jupyter lab

Requirements: Python 3.9-3.12, NumPy (1.x or 2.x), SciPy, Matplotlib, JupyterLab, and PyTorch (CPU build is enough; only Part 3 needs it). No GPU, internet connection or data files are needed.

How to use

• Run the cells from top to bottom with Shift+Enter, or use Kernel > Restart Kernel and Run All Cells... (about 1.5 minutes in total; almost all of it is the PINN training in Section 3.6, about 1 minute).
• The notebook is delivered with its outputs saved, so it can be shown or read without running anything. For a clean student copy use Edit > Clear Outputs of All Cells (or jupyter nbconvert --clear-output --inplace Jupyter_in_Teaching_FEM_and_PINNs.ipynb).
• Cells that only draw figures are collapsed; click the bar to the left of a cell to expand it.
• The movie in Section 2.5 is an HTML/JavaScript player. In a freshly opened notebook it may only play after re-running that cell or trusting the notebook (File > Trust Notebook).
• On a slow laptop, halve n_adam and n_lbfgs in the CONFIG cell of Section 3.5.

Files

Jupyter-share/
|-- Jupyter_in_Teaching_FEM_and_PINNs.ipynb   # the merged 60-minute notebook (main file)
|-- README.md
|-- requirements.txt                           # pip dependencies
|-- environment.yml                            # conda environment "jshare"

Saved outputs were produced with Python 3.10, NumPy 1.26, SciPy 1.13, Matplotlib 3.8 and PyTorch 2.2 (CPU). Timings and the last digits of the PINN errors differ slightly between machines.