Use Literate.jl to incorporate examples into documentation via CI

[MikaelSlevinsky]

I was inspired by https://github.com/FourierFlows/FourierFlows.jl, in particular the example they have (https://github.com/FourierFlows/FourierFlows.jl/blob/master/examples/OneDShallowWaterGeostrophicAdjustment.jl) that gets run as part of the documentation stage in GitHub Actions in every commit. The very nice result is https://fourierflows.github.io/FourierFlowsDocumentation/dev/generated/OneDShallowWaterGeostrophicAdjustment/.

Did the same thing with the FastTransforms examples (since the docs are quite sparse), and I'm pretty pleased. The FourierFlows.jl scripts show that docs can be hosted in a separated repository, so probably it's possible for the examples here to be added to the ApproxFun.jl documentation website. Or alternatively, have a separated website repository be built from multiple GitHub sources (the source source and examples source).

[MikaelSlevinsky]

Actually, another benefit is that Literate.jl can create Jupyter notebooks from the same source as *.jl => Markdown => HTML. So all the notebooks in this repository could be significantly condensed into Julia scripts (which have a much smaller codeprint).