Posts
Fourier series widget
I wrote a widget which allows one to interactively watch a partial Fourier sum converge. In undergrad I was always sort of dubious that all functions (in $L_2$ space) could be represented by Fourier series, so I’m hoping this makes it a little bit more palatable. I still need to publish the widget (or one I rewrote in Rust) to Github pages, so the link is currently defunct.
Introduction to liquid crystals
This was an attempt to write a talk out as a post to try to curb some procrastination (really had some writer’s block making the slides). It was pretty silly, and I still need to put in the figures (right now it’s all placeholders), so the link is currently defunct.
Bachmann-Landau notation widget
I started reading Calculus and Analysis in Euclidean Space, one of the really great Undergraduate Texts in Mathematics to try to skirt around reading Calculus on Manifolds – it was just pretty terse and didn’t lay out a lot of the intuition. However, C&A in E starts off with Bachmann-Landau notation to simplify the presentation. I’ve thought some about trying to make more visual proofs of some of the theorems in the book (e.g. inverse function theorem, implicit function theorem), but I’m a little technically limited. As a first step, I started writing a widget in Typescript which allows the user to enter in an expression in $x$ and $y$, and then plots the image of a circle of radius $r$ as well as another circle. The user can then zoom in and also change the input circle radius. The idea is that one can graphically investigate the convergence properties of $2D$ functions to get a better intuition for the different asymptotic behaviors.