Iteration of Linear Differential Operators

This repository contains a University of Waterloo Directed Research Program project by Jake Edmonstone and Matthew Tchouikine, mentored by Paul Cusson.

The project begins with a question about repeatedly differentiating a smooth function: if the sequence of derivatives

$$ f(x), f'(x), f''(x), \ldots $$

converges pointwise, what can its limit be? The write-up proves that the limit must satisfy (g' = g), so it has the form (g(x) = Ce^x). It then studies analogous questions for first-order linear differential operators (L f = a f' + b f), including examples where the leading coefficient vanishes.

Files

• drp.typ — the full mathematical write-up and proofs.
• slides.typ — the presentation slides.

Building

The documents are written in Typst. With Typst installed, run:

typst compile drp.typ
typst compile slides.typ

This produces drp.pdf and slides.pdf in the repository root. The slides use the Typst packages touying, thmbox, and numbly, which Typst downloads automatically when needed.