Derivations, Not Just Simulations: Teaching Applied Mathematics with Scientific Python
summary
Presents a reproducible teaching pattern — Motivate, Symbolize, Derive, Lambdify, Simulate, Validate — implemented as Marimo notebooks using SymPy (senpai), NumPy, SciPy, matplotlib, tests and GitHub Actions for automated publishing. Works through Isaacs’ Homicidal Chauffeur: symbolic derivation yields a bang-bang controller for the car and a gradient-ascent evader with limit‑cycle behavior; expressions are lambdified to run ~80 initial conditions with interactive time‑sweep widgets, visual trajectories, and unit tests, letting code verify algebra and surface surprising joint‑optimal behaviors.
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chapters (14)
- 0:00Introduction and motivation
- 1:07Homicidal chauffeur game explained
- 3:15Symbolic math with SciPy tools
- 6:27Policies and optimal control
- 8:12Hamiltonian and co-state variables
- 10:17Bang-bang controller for pursuer
- 12:42Evader’s gradient ascent strategy
- 15:49Dispersal fields and limit cycles
- 17:14Visualizing trajectories with code
- 19:19Validating assumptions and math
- 21:04Model validation and regularity
- 22:09Teaching approach: motivate symbolize derive
- 23:35Q&A on model-based engineering
- 25:42Q&A on LLMs and symbolic math
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